function. Study Guide and Review - Chapter 4 State whether each sentence is true or false . If false , replace the underlined term to make a true sentence. 2. The process of using a linear equation to make predictions about values that are beyond the range of the data is called linear regression. SOLUTION: The statement is false. The process of using a linear equation to make predictions about values that are beyond the range of the data is called linear extrapolation. Linear regression is an algorithm to find a precise line of fit for a set of data. 4. The correlation coefficient describes whether the correlation between the variables is positive or negative and how closely the regression equation is modeling the data. SOLUTION: The range of a relation is the domain of the inverse of the relation. The statement is false. Write an equation of a line in slope-intercept form with the given slope and y-intercept. Then graph the equation. 10. slope: 3, y-intercept: 5 SOLUTION: The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept. To graph the equation, plot the y-intercept (0, 5). Then move down 3 units and left 1 unit. Plot the point. Draw a line through the two points. SOLUTION: The correlation coefficient describes whether the correlation between the variables is positive or negative and how closely the equation is modeling the data. So, the statement is true. 6. Lines that intersect at acute angles are called perpendicular lines. SOLUTION: The statement is false. Lines that intersect at right angles are called perpendicular lines. Acute angles have measures less than 90. 8. The range of a relation is the range of its inverse function. SOLUTION: The range of a relation is the domain of the inverse of the relation. The statement is false. 12. slope: , y-intercept: 3 SOLUTION: The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y -intercept. Write an equation of a line in slope-intercept form with the given slope and y-intercept. Then graph the equation. 10. slope: 3, y-intercept: 5 SOLUTION: The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept. To graph the equation, plot the y-intercept (0, 3). Then move up 2 units and right 3 units. Plot the point. Draw a line through the two points. To graph the equation, plot the y-intercept (0, 5). left 1 unit. Plot the point. Draw a line through the two points. ThenManual move- Powered down 3 by units and eSolutions Cognero Page 1 Study Guide and Review - Chapter 4 12. slope: , y-intercept: 3 SOLUTION: The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y -intercept. 16. SOLUTION: To graph the equation, plot the y-intercept (0, 1). Then move up 1 unit and right 2 units. Plot the point. Draw a line through the two points. To graph the equation, plot the y-intercept (0, 3). Then move up 2 units and right 3 units. Plot the point. Draw a line through the two points. 18. SKI RENTAL Write an equation in slope-intercept form for the total cost of skiing for h hours with one lift ticket. Graph each equation. 14. y = 4x − 2 SOLUTION: To graph the equation, plot the y-intercept (0, −2). Then move up 4 units and right 1 unit. Plot the point. Draw a line through the two points. SOLUTION: The rate of $5 per hour represents the rate or slope. The cost of the lift ticket is a constant $15, no matter how many hours you ski. So, the total cost of skiing for h hours can be written as y = 5h + 15. Write an equation of the line that passes through the given point and has the given slope. 20. (2, −6), slope −4 SOLUTION: Find the y-intercept. Write the equation in slope-intercept form. 16. SOLUTION: To graph the equation, plot the y-intercept (0, 1). Then move up 1 unit and right 2 units. Plot the point. Draw a line through the two points. eSolutions Manual - Powered by Cognero Page 2 22. (5, −2), slope SOLUTION: The rate of $5 per hour represents the rate or slope. The cost of the lift ticket is a constant $15, no matter how manyand hours you ski. So, the total Study Guide Review - Chapter 4 cost of skiing for h hours can be written as y = 5h + 15. Write an equation of the line that passes through the given point and has the given slope. 20. (2, −6), slope −4 SOLUTION: Find the y-intercept. Write an equation of the line that passes through the given points. 24. (−4, 3), (1, 13) SOLUTION: Find the slope of the line containing the given points. Write the equation in slope-intercept form. Use the slope and either of the two points to find the y-intercept. 22. (5, −2), slope SOLUTION: Find the y-intercept. Write the equation in slope-intercept form. 26. (2, 4), (7, 2) SOLUTION: Find the slope of the line containing the given points. Write the equation in slope-intercept form. Write an equation of the line that passes through the given points. 24. (−4, 3), (1, 13) SOLUTION: Find the slope of the line containing the given points. Use the slope and either of the two points to find the y-intercept. eSolutions Manual - Powered by Cognero Page 3 Write the equation in slope-intercept form. SOLUTION: Study Guide and Review - Chapter 4 26. (2, 4), (7, 2) SOLUTION: Find the slope of the line containing the given points. Write each equation in standard form. 32. y − 7 = −3(x + 1) SOLUTION: 34. y − 9 = (x + 2) Use the slope and either of the two points to find the y-intercept. SOLUTION: Write the equation in slope-intercept form. Write each equation in slope-intercept form. 36. y − 12 = −2(x − 3) SOLUTION: Write an equation in point-slope form for the line that passes through the given point with the slope provided. 28. (6, 3), slope 5 38. y − 4 = (x + 2) SOLUTION: SOLUTION: 30. (−4, 2), slope 0 SOLUTION: Write each equation in standard form. 32. y − 7 = −3(x + 1) SOLUTION: eSolutions Manual - Powered by Cognero Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of each equation. 40. (0, 3), y = 3x + 5 SOLUTION: The slope of the line with equation y = 3x + 5 is Page 3. 4 The line parallel to y = 3x + 5 has the same slope, 3. Study Guide and Review - Chapter 4 Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of each equation. 40. (0, 3), y = 3x + 5 SOLUTION: The slope of the line with equation y = 3x + 5 is 3. The line parallel to y = 3x + 5 has the same slope, 3. Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation. 44. (1, 3), y = −2x − 4 SOLUTION: The slope of the line with equation y = −2x − 4 is −2. The slope of the perpendicular line is the opposite reciprocal of −2, or . 42. (−5, −2), y = x+4 SOLUTION: The slope of the line with equation y = x + 4 is 46. (3, 0), y = . The line parallel to y = x x + 4 has the same SOLUTION: slope, . The slope of the line with equation y = x is . The slope of the perpendicular line is the opposite reciprocal of , or 2. Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation. 44. (1, 3), y = −2x − 4 SOLUTION: The slope of the line with equation y = −2x − 4 is −2. The slope of the perpendicular line is the opposite reciprocal of −2, or 48. ATTENDANCE A scatter plot of data compares the number of years since a business has opened and its annual number of sales. It contains the ordered pairs (2, 650) and (5, 1280). Write an equation in slope-intercept form for the line of fit for this situation. SOLUTION: Find the slope of the line containing the given points. . eSolutions Manual - Powered by Cognero Page 5 of fit. Study Guide and Review - Chapter 4 48. ATTENDANCE A scatter plot of data compares the number of years since a business has opened and its annual number of sales. It contains the ordered pairs (2, 650) and (5, 1280). Write an equation in slope-intercept form for the line of fit for this situation. SOLUTION: Find the slope of the line containing the given points. 50. MOVIES The table shows ticket sales at a certain theater during the first week after a movie opened. Write an equation of the regression line. Then estimate the daily ticket sales on the 15th day. SOLUTION: Use a calculator to find the equation of the regression line. Use the slope and either of the two points to find the y-intercept. y = −5.79x + 99.14 To estimate the daily ticket sales on the 15th day, evaluate the regression equation for x = 15. Write the equation in slope-intercept form for the line of fit. 50. MOVIES The table shows ticket sales at a certain theater during the first week after a movie opened. Write an equation of the regression line. Then estimate the daily ticket sales on the 15th day. SOLUTION: Use a calculator to find the equation of the regression line. The daily ticket sales on the 15th day after a movie opens is $12.29. Find the inverse of each relation. 52. {(1, 9), (13, 26), (–3, 4), (–11, –2)} SOLUTION: To find the inverse, exchange the coordinates of the ordered pairs. eSolutions Manual - Powered by Cognero (1, 9) → (9, 1) (13, 26) → (26, 13) Page 6 (–4, –4) → (–4, –4) (0, –8) → (–8, 0) The daily and ticket sales on- Chapter the 15th day Study Guide Review 4 after a movie opens is $12.29. Find the inverse of each relation. 52. {(1, 9), (13, 26), (–3, 4), (–11, –2)} The inverse is {(4, -12), (0, -8), (-4, -4), (-8, 0)}. Find the inverse of each function 56. f (x) = 3x + 8 SOLUTION: To find the inverse, exchange the coordinates of the ordered pairs. SOLUTION: (1, 9) → (9, 1) (13, 26) → (26, 13) (–3, 4) → (4, –3) Write the final equation in slope-intercept form. So, (–11, –2) → (–2, –11) . The inverse is {(9, 1), (26, 13), (4, -3), (-2, -11)}. 58. SOLUTION: 54. SOLUTION: To find the inverse, exchange the coordinates of the ordered pairs. Write the final equation in slope-intercept form. So, f (–12, 4) → (4, –12) -1 (x) = 4x + 28. (–8, 0) → (0, –8) 60. (–4, –4) → (–4, –4) SOLUTION: (0, –8) → (–8, 0) The inverse is {(4, -12), (0, -8), (-4, -4), (-8, 0)}. Find the inverse of each function 56. f (x) = 3x + 8 SOLUTION: Write the final equation in slope-intercept form. So, . eSolutions Manual - Powered by Cognero Write the final equation in slope-intercept form. So, . Page 7
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