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Writing Linear Equations
Point-Slope Form
Click here to play
tutorial introduction
Standard (General) Form
Slope-Intercept Form
By Lindsay Hojnowski (2014)
Buffalo State College
04/2014
L. Hojnowski © 2014
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Aim for the Target
Learning Objectives
• The learner will be able to write a linear equation given a point and
the slope with 85% degree of accuracy using slope-intercept form.
• The learner will be able to write the linear equations given two
points with 85% degree of accuracy using slope-intercept form.
• Students will be able to write a linear equation in point-slope form
given a point and the slope 90% of the time.
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L. Hojnowski © 2014
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Learning Objectives Continued…
• Given an equation in point-slope form, students will be
able to change the equation into slope-intercept form 80%
of the time.
• Given an equation in point-slope form, students will be
able to change the equation into standard form 80% of the
time.
Aim for the Target
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L. Hojnowski © 2014
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Menu
Slope-Intercept Form- Given
the slope and a point
Given two points- Example 3
Quiz Question #1
Slope-Intercept Form
Example 1
Point-Slope Form
Quiz Question #2
Slope-Intercept Form
Example 2
Point-Slope Form Example
1 and 2
Quiz Question #3
Slope-Intercept Form
Example 3 and 4
Point-Slope  Standard
Form Example 1
Quiz Question #4
Slope-Intercept Form- Given
two points
Point-Slope  Standard
Form Example 2
Quiz Question #5
Given two points- Example 1
Point-Slope  SlopeIntercept Form Example 1
Quiz Question #6
Given two points- Example 2
Point-Slope  SlopeIntercept Form Example 2
Quiz Question #7
References
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Writing Equations in Slope-Intercept Form
Given the slope and a point
STEPS:
1)
2)
3)
4)
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Identify x, y, and m
Plug these values into y = mx + b
Solve for b
Write the answer in slope-intercept form (y = mx+b)
Slope-intercept form
L. Hojnowski © 2014
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Given a Point and Slope Example 1
STEPS:
1) Identify x, y, and m
2) Plug these values into y = mx + b
3) Solve for b
4) Write the answer in slope-intercept form (y = mx+b)
Steps to writing linear equations
Example 1: Write the equation of the line that passes through (2, 1) with a slope of 3
1) x = 2, y = 1 and m = 3
2) y = mx + b
1 = 3(2)+ b
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3) 1 = 6 + b
-6 -6
-5 = b
4) y = mx + b
y = 3x - 5
L. Hojnowski © 2014
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Given a Point and Slope Example 2
STEPS:
1) Identify x, y, and m
2) Plug these values into y = mx + b
3) Solve for b
4) Write the answer in slope-intercept form (y = mx+b)
Yintercept
and slope
Example 2: Write the equation of the line that passes through (5, -2) with a slope of 1/3.
1) x = 5, y = -2 and m = 1/3
2) y = mx + b
-2 = 3(1/3)+ b
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3) -2 = 1 + b
-1 -1
-3 = b
4) y = mx + b
y = 1/3x - 3
L. Hojnowski © 2014
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Given a Point and Slope Example 3 and 4
Example 3: (8, 3) and m = 1
Example 4: (-6, 7) and m = 0
STEP 1: x = 8, y = 3, m = 1
STEP 1: x = -6, y = 7, m = 0
STEP 2:
y = mx + b
3 = 1(8) + b
3=8+b
-8 -8
-5 = b
STEP 2:
y = mx + b
y=x-5
STEP 4:
STEP 3:
STEP 4:
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y = mx + b
7 = 0(-6) + b
7=0+b
STEP 3: **Anything times zero is zero**
7=b
L. Hojnowski © 2014
y = mx + b
y=7
Horizontal line
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Writing Equations in Slope-Intercept Form
Given two points
STEPS:
1) Use the slope formula to find m
2) Choose one of the given points (the easier one) and
plug x, y, and m into y = mx + b
3) Solve for b
4) Write the answer in slope-intercept form (y = mx+b)
Two Points
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L. Hojnowski © 2014
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Given Two Points Example 1
STEPS:
1) Use the slope formula to find m
2) Choose one of the given points (the easier one) and plug x, y, and m into y = mx + b
3) Solve for b
4) Write the answer in slope-intercept form (y = mx+b)
Example 1: Write the equation of the line that passes through (3, 1) and (2, 4)
1) m = y2 – y1
x2 – x1
2) (3, 1)
y = mx + b
1 = -3 (3) + b
m= 4–1
2–3
m = -3
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3) 1 = -9 + b
+9 +9
10 = b
4) y = mx + b
y = -3x +10
L. Hojnowski © 2014
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Given Two Points Example 2
STEPS:
1) Use the slope formula to find m
2) Choose one of the given points (the easier one) and plug x, y, and m into y = mx + b
3) Solve for b
4) Write the answer in slope-intercept form (y = mx+b)
Example 2: Write the equation of the line that passes through (-4, -2) and (-5, -6)
1) m = y2 – y1
x2 – x1
2) (-4, -2)
y = mx + b
-2 = 4(-4) + b
m = -6 – -2
-5 – -4
m = -4
-1
m = 4
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3) -2 = -16+ b
+16 +16
14 = b
4) y = mx + b
y = 4x + 14
L. Hojnowski © 2014
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Given Two Points Example 3
Example 3: Write the equation of the line that passes through (3, 5) and (-2, 2)
1) m = y2 – y1
x2 – x1
m=
2) (3, 5)
y = mx + b
5 = 3/5(3) + b
2–5
-2 – 3
m = -3
-5
m = 3
5
3) 5 = 9/5 + b
-9/5 -9/5
16/5 = b
4) y = mx + b
y = 3/5x + 16/5
Slop Formula
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Point-Slope Form
• Point-Slope Formula: y- y1 = m (x – x1)
– Use this formula when you are given a point and a slope
– Also use this formula when the question tells you too (READ CAREFULLY!)
– Click on the picture below to see a video on how to use the point-slope formula
Point-Slope Formula
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Point-Slope Form Example 1 and 2
Point-Slope Formula
Example 1: Write an equation in pointslope from for the line that passes
through the point (-2, 1) and has a
slope of -6.
y – y1 = m (x – x1)
y – 1 = -6 (x - - 2)
y – 1 = -6 (x + 2)
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Example 2: Write an equation in pointslope from for the line that passes
through the point (-2, -8) and has a
slope of 5/6.
y – y1 = m (x – x1)
y – -8 = 5/6 (x - - 2)
y + 8 = 5/6 (x + 2)
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Point-Slope  Standard Form Example 1
STEPS:
1) Distribute
2) Rewrite into standard form (Ax + By = C), identify A, B, and C
Example 1: Write y + 7 = 5 (x + 3) in standard form.
y + 7 = 5 (x + 3)
y + 7 = 5x + 15
Distribute
-7
-7
Get y by itself (7s cancel)
y = 5x + 8
Combine like terms
-5x -5x
Rewrite
into standard form
-5x + y = 8
A = -5, B = 1, C =
8
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Point-Slope  Standard Form Example 2
y – y = m (x – x )  Ax + By = C
Point-Slope Form  Standard Form
1
1
Example 2: Write y - 1= -2/3 (x - 5) in standard form.
y - 1= -2/3 (x - 5)
y - 1= (-2/3)x + 10/3
+1
+1
y = (-2/3)x + 13/3
+(2/3)x +(2/3)x
(2/3)x+ y = 13/3
3((2/3)x+ y = 13/3)
2x + 3y = 13
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Distribute
Get y by itself (1s cancel)
Combine like terms
Rewrite into standard form
**Standard form can only contain integers
(multiply the whole equation by 3)**
A = 2, B = 3, C = 13
L. Hojnowski © 2014
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Point-Slope  Slope-Intercept Example 1
STEPS:
1) Distribute
2) Rewrite into slope-intercept form (y = mx + b) and identify m (slope) and b (y-intercept)
Example 1: Write y + 3 = 3/2 (x + 1) in
slope-intercept form.
y + 3 = 3/2 (x + 1)
y + 3 = (3/2)x + 3/2
-3
-3
y = (3/2)x – 3/2
Or
y = 1.5x – 1.5
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Distribute
Get y by itself (3s cancel)
Combine like terms (slope-intercept form)
m = 3/2, b = 3/2
L. Hojnowski © 2014
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Point-Slope  Slope-Intercept Example 2
y – y = m (x – x )  Ax + By = C
Point-Slope Form  Standard Form
1
1
Example 2: Write y – 10 = 4 (x + 6) in slope-intercept form.
y – 10 = 4 (x + 6)
y – 10 = 4x + 24
+10
+10
y = 4x + 34
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Distribute
Get y by itself (10s cancel)
Combine like terms (slope-intercept form)
m = 4, b = 34
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Quiz Question #1
1. Which of the following formulas is slope-intercept form?
a. y = mx +b
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b. y – y1 = m (x – x1)
c. Ax + By = C
L. Hojnowski © 2014
d. y = ax2 + bx +c
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Quiz Question # 2
2. Write the equation of a line that passes through (2, 1) and has a slope
of 4. Your final answer should be in slope-intercept form.
a. y – 1 = 4 (x – 2)
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b. y = 4x – 7
c. -4x + y = -7
L. Hojnowski © 2014
d. y = -4x + 7
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Quiz Question # 3
3. Write the linear equation in point-slope form using the following
information:
(-7, 2), m = 6
a. y + 2 = 6 (x – 7)
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b. y - 2 = 6 (x + 7)
c. -6x + y = 44
L. Hojnowski © 2014
d. y = 6x + 44
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Quiz Question # 4
4. Using slope-intercept form, write the equation passing through the
points (-5, 3) and (0, -7).
a. y = 2x + 7
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b. y = 2x - 5
c. y = -2x - 5
L. Hojnowski © 2014
d. y = -2x - 7
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Quiz Question # 5
5. Write y – 10 = 2 (x – 8) in standard form.
a. 2x - y = 6
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b. 2x + y = 6
c. -2x + y = -6
L. Hojnowski © 2014
d. y = 2x -6
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Quiz Question # 6
6. Johnny wrote y + 4 = 2/3 (x + 7) in standard from as (-2/3)x + y = 2/3.
Jenna wrote the same equation in standard form and got 2x – 3y = -2.
Who is correct?
a. Johnny
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b. Jenna
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Quiz Question # 7
7. Write y + 6 = -3/4 (x + 8) in slope-intercept form.
a. y + 6 = (-3/4)x – 6
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b. y = (-3/4)x – 12
L. Hojnowski © 2014
c. y = (-3/4)x
d. y = (-3/4)x + 12
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Reference from the dictionary
References
• McGraw-Hill Companies. (2014). Glencoe Algebra 1 Common Core
Edition. New York: McGraw Hill.
• Seminars.usb.ac.ir. (2011). Hitting the objectives, Retrieved on
September 14th, 2012, from
• http://www.teambuildinggames.org/role-of-the-team-buildingfacilitator.
• Smiley Face, Retrieved on September 14th, 2012, from
http://ed101.bu.edu/StudentDoc/current/ED101fa10/rajensen/images
/happy-face1.png.
• Wee, E. (2011). Try again, Retrieved on September 15th, 2012, from
http://radionjournals.blogspot.com/2011/04/try-again-part-3-caringfor-children.html.
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