1. science
2. mathematics
3. algebra

Name ___________________________
Period__________
Date ___________
LF5
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STUDENT PAGES
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LINEAR FUNCTIONS
STUDENT PACKET 5: INTRODUCTION TO LINEAR FUNCTIONS
1
LF5.2 Equations of Lines in Different Forms
• Understand the standard form of a linear equation.
• Understand the point-slope form of a line
• Change one form of a linear equation to other forms
7
o
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LF5.1 Slope-Intercept Form
• Graph lines.
• Interpret the slope of the graph of a line.
• Find equations of lines.
• Use similar triangles to explain why the slope m is the same
between any two distinct points on a non-vertical line in the
coordinate plane.
17
LF5.4 Vocabulary, Skill Builders, and Review
21
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LF5.3 Graphing Inequalities in Two Variables
• Understand that the boundary line of a linear inequality is
represented by a linear equation
• Understand that the graph of a linear inequality is a half-plane.
Linear Function Unit (Student Packet)
LF5 – SP
Introduction to Linear Functions
WORD BANK
Definition or Explanation
Example or Picture
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Word or Phrase
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boundary line
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explicit rule
half plane
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linear function
N
linear inequality
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slope of a line
o
point-slope form of
a linear equation
slope-intercept
form of a linear
equation
m
standard form of a
linear equation
Sa
x-intercept
y-intercept
Linear Function Unit (Student Packet)
LF5 – SP0
Introduction to Linear Functions
5.1 Slope-Intercept Form
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SLOPE-INTERCEPT FORM
Set (Goals)
We will find equations of lines in slopeintercept form. We will extend the meaning
of slope to horizontal and vertical lines. We
will use properties of parallels and similar
triangles to deepen our understanding of
the meaning of slope of a line.
• Graph lines.
• Interpret the slope of the graph of a line.
• Find equations of lines.
• Use similar triangles to explain why the
slope m is the same between any two
distinct points on a non-vertical line in
the coordinate plane.
Go (Warmup)
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Label some points on this line.
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Ready (Summary)
x
m
1. When x = 0, then y = _______. This is called the _______________________.
2. Select two points on the line. Find the
difference in the y-coordinates
difference in the x-coordinates
as you move
Sa
from one point to another.
This is called the ________________________________________________.
Linear Function Unit (Student Packet)
LF5 – SP1
Introduction to Linear Functions
5.1 Slope-Intercept Form
FINDING EQUATIONS OF LINES
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1. Write the coordinates next to the labeled points.
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E
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A
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F
x
C
G
H
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B
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Slope-intercept form of a line: _______________________
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1. For Line AF
Slope: __________
y-intercept: __________
Equation: ____________________
Linear Function Unit (Student Packet)
LF5 – SP2
Introduction to Linear Functions
5.1 Slope-Intercept Form
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FINDING EQUATIONS OF LINES (continued)
Find the slope, the y-intercept, and the equation in slope-intercept form for each line on the
previous page.
2. Line DE
Slope: _____________
Slope: ______________
y-intercept: _________
y-intercept: __________
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Equation: ____________________
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Equation: ____________________
3. Line IK
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4. Line HG
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Slope: _____________
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1. Line BC
Slope: ______________
y-intercept: __________
Equation: ____________________
Equation: ____________________
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y-intercept: _________
Linear Function Unit (Student Packet)
LF5 – SP3
Introduction to Linear Functions
5.1 Slope-Intercept Form
FINDING MORE EQUATIONS
•
•
•
•
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Graph a line that fits each of these descriptions.
Find the slope, the y-intercept, and the equation of each line in slope-intercept form.
Use your equation to determine if a particular point lies on the line.
Find the x-intercept (the point where the graph crosses the x-axis, or x-value when
y = 0)
y
1. Graph the line that goes through
the origin and the point (5, 6).
y-intercept:_______
Equation: __________________
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Use your equation to show that the
point (-5,-6) lies on the line.
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Slope: _______
Graph the line that goes through
(-1, 2) and has a slope of 2
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2.
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x-intercept:_______
x
Slope: _______
y-intercept:_______
Equation: __________________
Use your equation to show that the
point (1, 2) does not lie on the line.
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x
x-intercept:_______
Linear Function Unit (Student Packet)
LF5 – SP4
Introduction to Linear Functions
5.1 Slope-Intercept Form
FINDING MORE EQUATIONS (continued)
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3.
Graph a line that fits each of these descriptions.
Find the slope, the y-intercept, and the equation of each line in slope-intercept form.
Use your equation to determine if a particular point lies on the line.
Find the x-intercept.
y
Graph the line that goes through
the points (2, 1) and (-2, 3).
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•
•
•
•
y-intercept:_______
Equation: __________________
x
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Use your equation to show that the
point (2, 4) does not lie on the line.
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Slope: _______
Graph the line that has intercepts
(0, -1) and (-4, 0).
y
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4.
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x-intercept:_______
Slope: _______
y-intercept:_______
Equation: __________________
Use your equation to show that the
point (4,-2) lies on the line.
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m
x
x-intercept:_______
Linear Function Unit (Student Packet)
LF5 – SP5
Introduction to Linear Functions
5.1 Slope-Intercept Form
HORIZONTAL AND VERTICAL LINES
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Q
P
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Y
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Two points on the
line
( ___, ___ )
( ___, ___ )

2. WY
( ___, ___ )
( ___, ___ )

3. LM
( ___, ___ )
( ___, ___ )

4. RS
( ___, ___ )
( ___, ___ )
y-intercept
slope
equation
y=
x=
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
1. PQ
x-intercept
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Line
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W
Sa
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5. What is the slope of a horizontal line?___________________. Can you write the equation
of a horizontal line in slope-intercept form? ______ Explain.
6. What is the slope of a vertical line?______________________. Can you write the equation
of a vertical line in slope-intercept form? _______ Explain.
Linear Function Unit (Student Packet)
LF5 – SP6
Introduction to Linear Functions
5.2 Equations of Lines in Different Forms
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EQUATIONS OF LINES IN DIFFERENT FORMS
Set (Goals)
We will review the slope-intercept form of a
linear function and learn about two other
forms of this equation: standard form, and
point-slope form.
• Understand the standard form of a linear
equation
• Understand the point-slope form of a
linear equation
• Change one form of a linear equation to
other forms
Go (Warmup)
y =-
2. Here is a graph of a linear equation.
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1. Here is an equation in
slope-intercept form.
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Ready (Summary)
2
x +1
3
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a. Slope: m = ________
b. The y-intercept is ________
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c. Graph the equation below
Linear Function Unit (Student Packet)
a. Slope: m = ________
b. The y-intercept is ________
c. The equation in slope-intercept form
is y = ________________
LF5 – SP7
Introduction to Linear Functions
5.2 Equations of Lines in Different Forms
STANDARD FORM
ax + by = c,
where a and b cannot both be equal to zero.
y = 3x + 2
2.
2x + y = 6
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1.
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Write the standard form and slope-intercept form for each equation below.
Note that it may already be in one of these forms.
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The standard form of a linear equation is
slope-intercept form:________________
N
slope-intercept form:________________
x = 2 – 4y
standard form: _____________________
4.
3x +
1
y–1 = 0
2
m
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3.
o
standard form: _____________________
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slope-intercept form:________________
standard form: _____________________
Linear Function Unit (Student Packet)
slope-intercept form:________________
standard form: _____________________
LF5 – SP8
Introduction to Linear Functions
5.2 Equations of Lines in Different Forms
REVISITING SLOPE: NEW NOTATION
m =
verticalchange
changein y
=
horizontalchange
changein x
=
Δy
Δx
=
( y 2 - y1 )
( x2 - x1 )
Figure
2
(5, 4)
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(5, 4)
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Figure
1
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∆ is the Greek letter “delta,” and here it stands for the words “change in.”
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Recall that the slope of a line (represented by m in the equation y = mx + b) is the ratio of
the vertical change to the horizontal change, often referred to as “rise over run.”
(1, -2)
N
(1, -2)
In figures 1 and 2 note the highlighted points and the directions of the dashed arrows.
1.
2.
Figure 2
(up) ______
(down) ______
b. count the horizontal change
(right) ______
(left) ______
c. write the slope
m=
m=
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a. count the vertical change
Figure 1
m =
verticalchange
Δy
=
horizontalchange
Δx
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m
3. Are the slope ratios you found in problems 1 and 2 equivalent or not? Explain.
4. What does
Δy
mean?
Δx
Linear Function Unit (Student Packet)
LF5 – SP9
Introduction to Linear Functions
5.2 Equations of Lines in Different Forms
REVISITING SLOPE: NEW NOTATION (continued)
y
A common way to refer to unknown
coordinates is to use subscript notation.
Refer to another point as (x2, y2).
•
The subscripts (the small 1 and 2) are
only for naming purposes.
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•
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Refer to one point as (x1, y1).
(x2, y2)
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•
(x1, y1)
Find the slope of the line given the points from the previous page, (5, 4) and (1, -2).
Note: either point can be named (x1 , y1) or (x2 , y2).
(x2 , y2) = (5, 4)
(x1 , y1) = (1, -2)
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5.
6.
(x2 , y2) = (1, -2)
(x1 , y1) = (5, 4)
difference between
y-coordinates (∆y = y2 – y1)
4 – (____) = ____
(____) – (____) = ____
b.
difference between
x-coordinates (∆x = x2 – x1)
5 – (____) = ____
(____) – (____) = ____
c.
m=
N
a.
y – y1
Δy
= 2
Δx
x2 – x1
m=
o
m=
The points (3, 2) and (0, 6) lie on a line. What is incorrect about the following slope
calculation?
Δy
6-2
4
m =
=
=
Δx
3-0
3
m
8.
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7. Are the ratios you found in problems 5 and 6 equivalent or not? Explain.
Explain why lining up the points in the following fashion might help to avoid the mistake
made above.
Sa
9.
(x2 , y2) = (0, 6)
(x1 , y1) = (3, 2)
Linear Function Unit (Student Packet)
LF5 – SP10
Introduction to Linear Functions
5.2 Equations of Lines in Different Forms
SLOPE: NEW NOTATION PRACTICE
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Given the following points on a line, (-1, 3) and (5, -5), find:
1. (x2 , y2) = (-1, 3)
(x1 , y1) = (5, -5)
2. (x2 , y2) = (5, -5)
(x1 , y1) = (-1, 3)
difference between
y-coordinates (∆y = y2 – y1)
(____) – (____) = ____
(____) – (____) = ____
b.
difference between
x-coordinates (∆x = x2 – x1)
(____) – (____) = ____
(____) – (____) = ____
c.
m=
m=
m=
3.
(x1, y1) →
(2, 5)
4.
m=
(_______)
=
(_______)
(0, -4)
m =
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m =
5.
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(-2, 3)
(-1, 6)
(_______)
=
(_______)
(0, 3)
(-2, 5)
m =
(_______)
=
(_______)
o
Δy
Δx
y 2 – y1
=
x2 – x1
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For the given pairs of points on a line, find the slope.
(x2, y2) →
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y – y1
Δy
= 2
Δx
x2 – x1
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a.
6. Two points on a line are (-5, 10) and (3, -6).
m
Place one ordered pair over the other to find m =
( y 2 - y1 )
Δy
=
Δx
( x2 - x1 )
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7. Jerome was given two points on a line, (-3, 0) and (4, -1).
To calculate the slope he did the following:
Linear Function Unit (Student Packet)
4 - (-3)
7
= . What was his mistake?
-1- (0) -1
LF5 – SP11
Introduction to Linear Functions
5.2 Equations of Lines in Different Forms
The slope of the line to the right is 2
•
One point identified on the line is (1, 4)
•
It is not obvious what the other highlighted
point is, so we will call it (x, y)
(x, y)
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•
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POINT-SLOPE FORM
(1, 4)
the point-slope form of a linear equation:
m=
y - ( ____ )
Δy
= 2
Δx
x2 - (____)
2.
2 =
( y )-(____)
(____)-(____)
3.

(2)( ______ ) = 

5.
substitution:
o

 ( ______ )

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4.
the slope formula
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1.
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y – y1 = m(x – x1)
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Fill in the blanks below to verify:
m = 2;
(x2, y2) = (x, y)
(x1, y1) = (1, 4)
multiplication property of equality:
multiply both sides by (x – 1)
2( x -1) = ( ______ )
simplify right side by multiplication
________ = 2( x - 1)
symmetric property of equality:
expressions “switch sides”
(This equation is now in point-slope
form.)
m
6. Look at the equation in problem.
a. Find the slope (m) and draw a small arrow pointing to it.
Sa
b. Find the known point on the line, (x1, y1) = (1, 4), and underline each coordinate value.
c. Find the unknown point on the line, (x2, y2) = (x, y), and circle each coordinate value.
d. Write the equation of this line in slope-intercept form.
Linear Function Unit (Student Packet)
LF5 – SP12
Introduction to Linear Functions
5.2 Equations of Lines in Different Forms
POINT-SLOPE FORM (continued)
8. The standard form of a linear equation is __________________
9. The slope-intercept form of a linear equation is _________________
point-slope form:
11.Given: m = 5 and one
point on the line is
(2, -6)
point-slope form:
slope-intercept form:
slope-intercept form:
12.m = 1 and one point on
the line is (0, -5)
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10. Given: m = -3 and one
point on the line is (5, 4)
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Write the equations of the lines in the following forms in any order desired.
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7. The point-slope form of a linear equation is _________________
slope-intercept form:
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point-slope form:
standard form:
standard form:
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standard form:
Linear Function Unit (Student Packet)
LF5 – SP13
Introduction to Linear Functions
5.2 Equations of Lines in Different Forms
Find equations of lines in different forms. Use the information given.
1. Given:
2. Given:
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PRACTICE WITH DIFFERENT FORMS
(-2, 3) is on the line; slope =
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m = -2; y-intercept is 3
1
2
slope-intercept form
N
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slope-intercept form
point-slope form
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o
point-slope form
standard form
Sa
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standard form
Linear Function Unit (Student Packet)
LF5 – SP14
Introduction to Linear Functions
5.2 Equations of Lines in Different Forms
Find equations of lines in different forms. Use the information given.
3. Given:
4. Given (table):
y
-6
1
-3
2
0
3
3
4
6
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x
0
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(4, 3) and (-4, -5) are on the line
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PRACTICE WITH DIFFERENT FORMS (continued
slope-intercept form
N
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slope-intercept form
point-slope form
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point-slope form
standard form
Sa
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standard form
Linear Function Unit (Student Packet)
LF5 – SP15
Introduction to Linear Functions
5.2 Equations of Lines in Different Forms
Find equations of lines in different forms. Use the information given.
5. Given:
6. Given:
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(0, -2) and (-2, 0) are on the line
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PRACTICE WITH DIFFERENT FORMS (continued)
slope-intercept form
N
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slope-intercept form
point-slope form
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point-slope form
standard form
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standard form
Linear Function Unit (Student Packet)
LF5 – SP16
Introduction to Linear Functions
5.3 Graphing Inequalities in Two Variables
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GRAPHING INEQUALITIES IN TWO VARIABLES
Ready (Summary)
Set (Goals)
• Understand that the boundary line of a
linear inequality is represented by a
linear equation
• Understand that the graph of a linear
inequality is a half-plane
Go (Warmup)
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We will graph linear inequalities in two
variables by graphing dashed or solid
boundary lines and then shading halfplanes appropriately.
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Fill in the table below by writing the inequality in symbols, graphing it, and testing a number.
These inequalities are in one variable.
Words
Symbols
The opposite of x is less
than or equal to -2
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2.
Test a Number
N
1. -4 is greater than x
Graph
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3. On a graph, what does a closed dot ( ) mean?
4. On a graph, what does an open dot ( ) mean?
Sa
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5. When solving an inequality, doing what to both sides causes the inequality symbol to
change direction?
Linear Function Unit (Student Packet)
LF5 – SP17
Introduction to Linear Functions
5.3 Graphing Inequalities in Two Variables
INEQUALITIES IN TWO VARIABLES: INTRODUCTION
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1. Graph the line y = x to the right.
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2. Write some points below in which
the y-coordinate is greater than the
x-coordinate. (Use simple numbers
that are between -5 and 5.)
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3. Graph a few of these points.
Describe where they lie in
relation to the y = x line.
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4. Write some points below in which the y-coordinate is less than the x-coordinate. (Use
simple numbers that are between -5 and 5.)
5. Graph a few of these points. Describe where they lie in relation to the y = x line.
7. Graph the inequality y ≤ x by first
graphing y = x, and then lightly shading
the region in which the
y-coordinates are less than the
x-coordinates. The shaded region is
called a half plane.
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6. Graph the inequality y ≥ x by first
graphing y = x, and then lightly shading
the region in which the
y-coordinates are greater than the
x-coordinates. The shaded region is
called a half plane.
Test an ordered pair by substituting the x and Test an ordered pair by substituting the x and
y values into the inequality.
y values into the inequality.
Linear Function Unit (Student Packet)
LF5 – SP18
Introduction to Linear Functions
5.3 Graphing Inequalities in Two Variables
INEQUALITIES IN TWO VARIABLES: PRACTICE 1
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When graphing an inequality, its boundary line is solid when all of the points on the
line are included in the solution set of the inequality (similar to the closed dot on a
number line). The boundary line is dashed when the points on the line are not
included (similar to the open dot on a number line).
1. 2x – y > 4
1
x–1
3
4. y – 3 ≥
1
(x – 4)
2
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3. –y < 2(x – 1)
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2. y ≤ -
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Graph each inequality (slope-intercept form of a line tends to be easier to graph).
• Consider the equation of the boundary line and graph it as a solid or dashed line.
• Shade the appropriate half-plane.
• Test at least one point by substituting it into the inequality.
Linear Function Unit (Student Packet)
LF5 – SP19
Introduction to Linear Functions
5.3 Graphing Inequalities in Two Variables
INEQUALITIES IN TWO VARIABLES: PRACTICE 2
2.
4.
5.
3.
6.
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1.
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Write an inequality to match each graph.
Linear Function Unit (Student Packet)
LF5 – SP20
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
Across
Down
line that separates plane into two
half planes
1
a number that describes the “slant”
of a line
another name for input-output rule
2
a form of a linear equation:
y2 – y1 = m(x2 – x1) (2 words)
10 a form of the linear function of the
form: y = mx + b (2 words)
3
2x – 3y > 5 is an example of a
linear ________
11 a form of linear equation:
ax + by = c
4
another name for the shaded portion
of a linear inequality
6
(0, 7) is an example of
a(n) ___ - intercept
8
(-8, 0) is an example of
a(n) ___ - intercept
9
a function whose graph is a line
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7
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FOCUS ON VOCABULARY
Linear Function Unit (Student Packet)
LF5 – SP21
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
SKILL BUILDER 1
Draw line segments with the following
slopes.
L
od
2
1. Line AB with a slope of
.
1
A
-1
.
3
P
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2. Line CD with a slope of
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Complete.
C
1
.
4
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3. Line LM with a slope of
N
4. Line PQ with a slope of -3.
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1. E(2, -1) and F(7, 3)
o
Given each set of ordered pairs,
find the slope of the line that goes
through them.
2. G(-1, 1) and H(-2, 8)
m
3. J(-1, -3) and K(-7, 1)
Sa
4. N(2, 6) and R(7, 6)
Linear Function Unit (Student Packet)
LF5 – SP22
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
SKILL BUILDER 2
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1. The lengths of the sides of a pentagon are consecutive odd numbers. The perimeter is
435 cm. Find the length of each side of the pentagon.
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2. Arnon and Bob are taking the train from Los Angeles to San Francisco. Arnon leaves
the train station in Los Angeles at 8:00 AM on a slow train traveling 40 mph. Bob leaves
Los Angeles at 1 PM on a fast train traveling 75 mph. If it is 400 miles from Los
Angeles to San Francisco, who arrives first? Show your work and explain your
reasoning.
Linear Function Unit (Student Packet)
LF5 – SP23
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
SKILL BUILDER 3
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1. Draw a line through point A (1, 2)
2
with a slope of .
1
What is the y-intercept? ________
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2. Draw a line through point B (-2, -2)
-1
with a slope of .
3
What is the x-intercept? ________
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3. Draw a line through point C (4, 4)
1
with a slope of .
4
Name a point on this line
that is in the 2nd quadrant. ________
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5. S(5, 4) and T(2, 3)
o
Given each set of ordered pairs, use the slope formula to find the slope of the line that goes
through them.
8. Y(-5, -8) and Z(0, -12)
Sa
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7. W(10, 16) and X(-2, -4)
6. U(2, 10) and V(5, 1)
Linear Function Unit (Student Packet)
LF5 – SP24
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
SKILL BUILDER 4
Use for problems 1-6:
1. Slope of AB: ________________________
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2. Slope of AC: _______________________
3. Slope of BC: _______________________
B
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 _______

 _______
C
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4. Slope of DB: _______________________
5. Label and identify three similar right triangles
using a portion of the line as the hypotenuse
and horizontal and vertical segments for legs.
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Compute.
What is true about the ratio of corresponding
legs in these triangles?
Use for problems 7-10:
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6. What do you notice about the slope of each
line segment?
y
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7. Locate a point F so that the slope of line
-2
. Then draw line EF.
EF =
1
E
8. Name these points on your line.
F (____,____)
G ( 0 ,____)
H (____, 0 )
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E (____,____)
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9. Find the slope of line EH.
10. Find the equation of line EH in slope-intercept
form.
y = _______________________________
Linear Function Unit (Student Packet)
LF5 – SP25
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
SKILL BUILDER 5
(4, -2) and (-4, 0)
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1. Two points on
the line
Slope
y-intercept
2. Two points on
the line
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Equation of the
line in the form
y = mx + b
(-2, -3) and (1, -6)
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Slope
y-intercept
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Equation of the
line in the form
y = mx + b
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3. Complete the table, graph the values, and write an equation for the line that fits the data in
slope-intercept form.
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There are 4 quarts in 1 gallon.
Gallons (x)
0
1
1.5
Quarts (y)
0
4
6
2
2.75
3
x
y = _____________________________
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4. Does connecting your points with a line
make sense? Explain.
Linear Function Unit (Student Packet)
LF5 – SP26
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
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SKILL BUILDER 6
(1, 5)
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1. (-3, 1)
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Draw the following lines on the coordinate axes above. Then fill in the table.
two points
equation of the line in
y-intercept
slope
x-intercept
on the line
slope-intercept form
______
3. (-2, 4)
______
1
4. _____
______
-
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2. (-3, 9)
2
(6, -4)
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5. (-3, -1)
1
2
0
Linear Function Unit (Student Packet)
LF5 – SP27
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
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SKILL BUILDER 7
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Draw the following lines on the coordinate axes above. Then fill in the table.
One point
equation of the line in
y-intercept
slope
x-intercept
on the line
slope-intercept form
2.
3.
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-3
(4, -3)
2
m
4.
(1, 1)
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1.
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5.
Linear Function Unit (Student Packet)
3
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1
2
y = -3x + 4
1
y = - x–4
3
LF5 – SP28
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
SKILL BUILDER 8
Given
Form of linear equation
slope-intercept
standard
point-slope
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1. y- intercept is
-2
4
slope =
3
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Find equations of lines in different forms. Use the information given.
2. slope = -3;
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(1, -1) is on
the line;
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3. (3, -1) and
(6, 1) are
on the line
Linear Function Unit (Student Packet)
LF5 – SP29
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
SKILL BUILDER 9
Given
Form of linear equation
Slope-intercept
Standard
1. table
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y
-1
1
3
5
7
Point-slope
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x
0
1
2
3
4
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Find equations of lines in different forms. Use the information given.
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2. Graph
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3. (2, -2) and
(-2, 2) are
on the line
Linear Function Unit (Student Packet)
LF5 – SP30
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
SKILL BUILDER 10
x is greater than -3
3.
the opposite of x is less
than or equal to -2
4.
4 is greater than x
5.
-1 is less than or equal
to the opposite of x.
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2.
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x is equal to -1
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1.
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Write each statement using symbols. If the variable is on the right side, change it to the left
side using appropriate properties. Then graph each.
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Graph each inequality. Be sure they are in slope-intercept form first.
7.
-5 y + x ≥ 10
2
6.
y > x -1
3
8. Describe the differences between the graph of an inequality in one variable and the graph
of an inequality in two variables.
Linear Function Unit (Student Packet)
LF5 – SP31
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
TEST PREPARATION
1. Find the slope of the line through the points (0, 3) and (-5, 0).
3
5
B.
-
3
5
C.
5
3
D.
-
5
3
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A.
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Show your work on a separate sheet of paper and choose the best answer.
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2. Which of the following best describes the slope of the line through the points (-3, 2)
and (-3, -3)?
Positive slope
B.
Negative slope
C.
Zero slope
D.
No slope
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A.
3. Which of these equations represents the line through the points (-5, 13) and (5, 3)?
A.
y = -x – 8
B.
y = x+ 8
C.
y=x–8
D.
y = -x + 8
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4. Which equation is equivalent to y - 5 = 3( x - 1) and is also in standard form?
D. 3x – y = -2
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C. -3x + y = -2
B. y = 3x + 2
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A. y = 3x – 2
5. Which statement about linear inequalities in NOT true?
A. The graph of a linear inequality is a half-plane.
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B. The boundary line of a linear inequality must be either dashed or solid.
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C. If the boundary line of a linear inequality is dashed, the points on the boundary
line are solutions to the inequality.
D. If a point on one side of the boundary line of a linear inequality is a solution, a
point on the other side is NOT a solution.
Linear Function Unit (Student Packet)
LF5 – SP32
Introduction to Linear Functions
5.4 Vocabulary, Skill Builders, and Review
KNOWLEDGE CHECK
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Show your work on a separate sheet of paper and write your answers on this page.
5.1: Slope Intercept Form
Find the equation of each line in slope-intercept form.
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1. A line through the point (-1, -1) with a slope of 3.
5.3: Equations of Lines in Different Forms
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2. A line with an x-intercept of -2 and a y-intercept of -4.
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3. Write the equations from problems 1 and 2 above in:
a. Point-slope form
b. Standard form
4. For the given input-output table to the right:
y
a. Write the equation in slope-intercept form
0
-2
b. Write the equation in standard form
1
c. Write the equation in point-slope form
2
-1
d. Graph the equation
3
-
4
0
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x
-1
1
2
1
2
5.4: Graphing Inequalities in Two Variables
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5. Graph each inequality.
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a. y ≤ - x +3
b. x - y < - 4
Linear Function Unit (Student Packet)
LF5 – SP33
Introduction to Linear Functions
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This page is left intentionally blank for notes.
Linear Function Unit (Student Packet)
LF5 – SP34
Introduction to Linear Functions
Sa
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This page is left intentionally blank for notes.
Linear Function Unit (Student Packet)
LF5 – SP35
Introduction to Linear Functions
Sa
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This page is left intentionally blank for notes.
Linear Function Unit (Student Packet)
LF5 – SP36
Introduction to Linear Functions
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HOME-SCHOOL CONNECTION
Here are some questions to review with your young mathematician.
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Use graph paper as needed for problems 1-4 to find the equation of each line in (a) slopeintercept form, (b) point-slope form, and (c) standard form.
1
and an x-intercept of 5.
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3. The line with a slope of -
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2. The line through the points (-3, 3) and (-2, 1).
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1. The line through the point (0, -2) with a slope of 4.
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4. The line through the points (3, 1) and (-5, 1).
5. Graph 4 x + 2y ≥ - 6
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Parent (or Guardian) signature ____________________________
Linear Function Unit (Student Packet)
LF5 – SP37
Introduction to Linear Functions
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COMMON CORE STATE STANDARDS – MATHEMATICS
SELECTED COMMON CORE STATE STANDARDS FOR MATHEMATICS
A-REI-10
A-REI-3
A-REI-12
Graph the solutions to a linear inequality in two variables as a half plane (excluding the
boundary in the case of a strict inequality), and graph the solution set to a system of linear
inequalities in two variables as the intersection of the corresponding half-planes
Graph linear and quadratic functions and show intercepts, maxima, and minima.
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F-IF-7a
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A-CED-4
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8.F.2
Use similar triangles to explain why the slope m is the same between any two distinct points on
a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the
origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Compare properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions). For example, given a linear function
represented by a table of values and a linear function represented by an algebraic expression,
determine which function has the greater rate of change.
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving
equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
Understand that the graph of an equation in two variables is the set of all its solutions plotted in
the coordinate plane, often forming a curve (which could be a line).
Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
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STANDARDS FOR MATHEMATICAL PRACTICE
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MP1 Make sense of problems and persevere in solving them.
MP2 Reason abstractly and quantitatively.
MP3 Construct viable arguments and critique the reasoning of others.
MP4 Model with mathematics.
MP5 Use appropriate tools strategically.
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MP6 Attend to precision.
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MP7 Look for and make use of structure.
MP8 Look for and express regularity in repeated reasoning.
Linear Function Unit (Student Packet)
LF5 – SP38