Study Guide and Review - Chapter 4
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1 State whether each sentence is true or false. If false, replace the underlined term to make a true sentence. 1. The y-intercept is the y-coordinate of the point where the graph crosses the y-axis. The y-intercept is the point where the graph crosses the y-axis. So, the statement is true. true 3. An inverse relation is the set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair of a relation. This is the definition of an inverse function. Therefore, the statement is true. true 5. Lines in the same plane that do not intersect are called parallel lines. Lines in the same plane that do not intersect are called parallel lines. So, the statement is true. true 7. A(n) constant function can generate ordered pairs for an inverse relation. A constant function has the same function value for every element of the domain. An inverse function can generate ordered pairs for an inverse relation. So, the statement is false. Replace constant function with inverse function to make it a true statement. false, inverse function 9. An equation of the form y = mx + b is in point-slope form. An equation in point slope form looks like y y 1 = m(x x 1 ). An equation in slope intercept form looks like y = mx + b. The statement is false. false, slope-intercept form esolutions Manual - Powered by Cognero Page 1
2 Write an equation of a line in slope-intercept form with the given slope and y-intercept. Then graph the equation. 11. slope: 2, y-intercept: 9 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, 9). Then move down 2 units and right 1 unit. Plot the point. Draw a line through the two points. y = 2x 9 esolutions Manual - Powered by Cognero Page 2
3 13. slope:, y-intercept: 2 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, 2). Then move down 5 units and right 8 units. Plot the point. Draw a line through the two points. y = x 2 esolutions Manual - Powered by Cognero Page 3
4 Graph each equation. 15. y = 3x + 5 To graph the equation, plot the y-intercept (0, 5). Then move down 3 units and right 1 unit. Plot the point. Draw a line through the two points. esolutions Manual - Powered by Cognero Page 4
5 17. 3x + 4y = 8 First, rewrite the equation in slope-intercept form by solving for y. To graph the equation, plot the y-intercept (0, 2). Then down 3 units and right 4 units. Plot the point. Draw a line through the two points. esolutions Manual - Powered by Cognero Page 5
6 Write an equation of the line that passes through the given point and has the given slope. 19. (1, 2), slope 3 Find the y-intercept. Write the equation in slope-intercept form. y = 3x ( 3, 1), slope Find the y-intercept. Write the equation in slope-intercept form. esolutions Manual - Powered by Cognero Page 6
7 Write an equation of the line that passes through the given points. 23. (2, 1), (5, 2) Find the slope of the line containing the given points. Use the slope and either of the two points to find the y-intercept. Write the equation in slope-intercept form. y = x 3 esolutions Manual - Powered by Cognero Page 7
8 25. (3, 5), (5, 6) Find the slope of the line containing the given points. Use the slope and either of the two points to find the y-intercept. Write the equation in slope-intercept form. esolutions Manual - Powered by Cognero Page 8
9 27. CAMP In 2005, a camp had 450 campers. Five years later, the number of campers rose to 750. Write a linear equation that represents the number of campers that attend camp. Let x be the number of years since Two points on the line are (0, 450) and (5, 750). Find the slope of the line. Use the slope and either of the two points to find the y-intercept. Write the equation in slope-intercept form. The number of campers that attend camp can be represented by the linear equation y = 60x y = 60x Write an equation in point-slope form for the line that passes through the given point with the slope provided. 29. ( 2, 1), slope 3 y 1 = 3(x + 2) esolutions Manual - Powered by Cognero Page 9
10 Write each equation in standard form. 31. y 3 = 5(x 2) 5x y = y + 4 = (x 3) x 2y = 11 Write each equation in slope-intercept form. 35. y 2 = 3(x 5) y = 3x 13 esolutions Manual - Powered by Cognero Page 10
11 37. y + 3 = 5(x + 1) y = 5x + 2 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. 39. (2, 5), y = x 3 The slope of the line with equation y = x 3 is 1. The line parallel to y = x 3 has the same slope, 1. y = x ( 4, 1), y = 2x 6 The slope of the line with equation y = 2x 6 is 2. The line parallel to y = 2x 6 has the same slope, 2. y = 2x 7 esolutions Manual - Powered by Cognero Page 11
12 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. 43. (2, 4), y = 3x + 1 The slope of the line with equation y = 3x + 1 is 3. The slope of the perpendicular line is the opposite reciprocal of 3, or. 45. ( 5, 2), y = x + 4 The slope of the line with equation y = x + 4 is. The slope of the perpendicular line is the opposite reciprocal of, or 3. y = 3x 13 esolutions Manual - Powered by Cognero Page 12
13 47. Determine whether the graph shows a positive, a negative, or no correlation. If there is a positive or negative correlation, describe its meaning. The graph shows a positive correlation. As the number of hours spent studying increases, the test scores increase. Positive; as the number of hours spent studying increases, the test scores increase. esolutions Manual - Powered by Cognero Page 13
14 49. SALE The table shows the number of purchases made at an outerwear store during a sale. Write an equation of the regression line. Then estimate the number of sales on day 10 of the sale. Use a calculator to find the equation of the regression line. y = 5.36x + 11 To estimate the number of sales on day 10 of the sale, evaluate the regression equation for x = 10. The number of sales on day 10 of the sale should be about 65. y = 5.36x + 11; 65 esolutions Manual - Powered by Cognero Page 14
15 Find the inverse of each relation. 51. {(7, 3.5), (6.2, 8), ( 4, 2.7), ( 12, 1.4)} To find the inverse, exchange the coordinates of the ordered pairs. (7, 3.5) (3.5, 7) (6.2, 8) (8, 6.2) ( 4, 2.7) (2.7, 4) ( 12, 1.4) (1.4, 12) The inverse is {(3.5, 7), (8, 6.2), (2.7, -4), (1.4, -12)}. {(3.5, 7), (8, 6.2), (2.7, 4), (1.4, 12)} 53. To find the inverse, exchange the coordinates of the ordered pairs. ( 4, 2.7) (2.7, 4) ( 1, 3.8) (3.8, 1) (0, 4.1) (4.1, 0) (3, 7.2) (7.2, 3) The inverse is {(2.7, -4), (3.8, -1), (4.1, 0), (7.2, 3)}. {(2.7, 4), (3.8, 1), (4.1, 0), (7.2, 3)} esolutions Manual - Powered by Cognero Page 15
16 55. Find the inverse of each function Write the final equation in slope-intercept form. So, f -1 (x) =. 57. Write the final equation in slope-intercept form. So,. esolutions Manual - Powered by Cognero Page 16
17 59. Write the final equation in slope-intercept form. So,. esolutions Manual - Powered by Cognero Page 17
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