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.
1. The y-intercept is the y-coordinate of the point where the graph crosses the y-axis.
SOLUTION: The y-intercept is the point where the graph crosses the y-axis. So, the statement is true.
ANSWER: 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.
SOLUTION: This is the definition of an inverse function.
Therefore, the statement is true.
ANSWER: true
5. Lines in the same plane that do not intersect are called parallel lines.
SOLUTION: Lines in the same plane that do not intersect are called parallel lines. So, the statement is true.
ANSWER: true
7. A(n) constant function can generate ordered pairs for an inverse relation.
SOLUTION: 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.
ANSWER: false, inverse function
9. An equation of the form y = mx + b is in point-slope form.
SOLUTION: An equation in point slope form looks like y – y 1 = m(x − x1). An equation in slope intercept form looks like y = mx +
b. The statement is false.
ANSWER: false, slope-intercept form
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
SOLUTION: The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y -intercept.
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An equation in point slope form looks like y – y 1 = m(x − x1). An equation in slope intercept form looks like y = mx +
b. The statement is false.
ANSWER: Study
Guide and Review - Chapter 4
false, slope-intercept form
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
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, −9). Then move down 2 units and right 1 unit. Plot the point. Draw a
line through the two points.
ANSWER: y = −2x − 9
13. slope:
, y-intercept: −2
SOLUTION: The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y -intercept.
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Study
Guide and Review - Chapter 4
13. slope:
, y-intercept: −2
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, −2). Then move down 5 units and right 8 units. Plot the point. Draw a
line through the two points.
ANSWER: y=
x−2
Graph each equation.
15. y = −3x + 5
SOLUTION: 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.
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Study Guide and Review - Chapter 4
Graph each equation.
15. y = −3x + 5
SOLUTION: 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.
ANSWER: 17. 3x + 4y = 8
SOLUTION: 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.
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Study Guide and Review - Chapter 4
17. 3x + 4y = 8
SOLUTION: 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.
ANSWER: Write an equation of the line that passes through the given point and has the given slope.
19. (1, 2), slope 3
SOLUTION: Find the y-intercept.
Write the equation in slope-intercept form.
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Study Guide and Review - Chapter 4
Write an equation of the line that passes through the given point and has the given slope.
19. (1, 2), slope 3
SOLUTION: Find the y-intercept.
Write the equation in slope-intercept form.
ANSWER: y = 3x − 1
21. (−3, −1), slope
SOLUTION: Find the y-intercept.
Write the equation in slope-intercept form.
ANSWER: Write an equation of the line that passes through the given points.
23. (2, −1), (5, 2)
SOLUTION: Find the slope of the line containing the given points.
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ANSWER: Study Guide and Review - Chapter 4
Write an equation of the line that passes through the given points.
23. (2, −1), (5, 2)
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.
Write the equation in slope-intercept form.
ANSWER: y=x−3
25. (3, 5), (5, 6)
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.
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ANSWER: Study
y =Guide
x − 3 and Review - Chapter 4
25. (3, 5), (5, 6)
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.
Write the equation in slope-intercept form.
ANSWER: 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.
SOLUTION: Let x be the number of years since 2005. 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.
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ANSWER: Study Guide and Review - Chapter 4
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.
SOLUTION: Let x be the number of years since 2005. 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 + 450.
ANSWER: y = 60x + 450
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
SOLUTION: ANSWER: y − 1 = −3(x + 2)
Write each equation in standard form.
31. y − 3 = 5(x − 2)
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ANSWER: Study
and+Review
- Chapter 4
y −Guide
1 = −3(x
2)
Write each equation in standard form.
31. y − 3 = 5(x − 2)
SOLUTION: ANSWER: 5x − y = 7
33. y + 4 =
(x − 3)
SOLUTION: ANSWER: x − 2y = 11
Write each equation in slope-intercept form.
35. y − 2 = 3(x − 5)
SOLUTION: ANSWER: y = 3x − 13
37. y + 3 = 5(x + 1)
SOLUTION: ANSWER: eSolutions
Manual - Powered by Cognero
y = 5x + 2
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ANSWER: Study
and Review - Chapter 4
y =Guide
3x − 13
37. y + 3 = 5(x + 1)
SOLUTION: ANSWER: 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
SOLUTION: The slope of the line with equation y = x − 3 is 1. The line parallel to y = x − 3 has the same slope, 1.
ANSWER: y=x+3
41. (−4, 1), y = −2x − 6
SOLUTION: The slope of the line with equation y = −2x − 6 is −2. The line parallel to y = −2x − 6 has the same slope, −2.
ANSWER: y = −2x − 7
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
SOLUTION: 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 − .
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ANSWER: Study
Guide and Review - Chapter 4
y = −2x − 7
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
SOLUTION: 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 − .
ANSWER: 45. (−5, 2), y =
x+4
SOLUTION: The slope of the line with equation y =
x + 4 is
. The slope of the perpendicular line is the opposite reciprocal of
, or −3.
ANSWER: y = −3x − 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.
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SOLUTION: The graph shows a positive correlation. As the number of hours spent studying increases, the test scores increase.
ANSWER: Study
Guide and Review - Chapter 4
y = −3x − 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.
SOLUTION: The graph shows a positive correlation. As the number of hours spent studying increases, the test scores increase.
ANSWER: Positive; as the number of hours spent studying increases, the test scores increase.
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.
SOLUTION: 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.
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SOLUTION: The graph shows a positive correlation. As the number of hours spent studying increases, the test scores increase.
ANSWER: Study
Guide and Review - Chapter 4
Positive; as the number of hours spent studying increases, the test scores increase.
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.
SOLUTION: 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.
ANSWER: y = 5.36x + 11; 65
Find the inverse of each relation.
51. {(7, 3.5), (6.2, 8), (–4, 2.7), (–12, 1.4)}
SOLUTION: To find the inverse, exchange the coordinates of the ordered pairs.
(7, 3.5) → (3.5, 7)
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(6.2, 8) → (8, 6.2)
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The number of sales on day 10 of the sale should be about 65.
ANSWER: Study
Guide and Review - Chapter 4
y = 5.36x + 11; 65
Find the inverse of each relation.
51. {(7, 3.5), (6.2, 8), (–4, 2.7), (–12, 1.4)}
SOLUTION: 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)}. ANSWER: {(3.5, 7), (8, 6.2), (2.7, −4), (1.4, −12)}
53. SOLUTION: 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)}. ANSWER: {(2.7, −4), (3.8, −1), (4.1, 0), (7.2, 3)}
Find the inverse of each function
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The inverse is {(2.7, -4), (3.8, -1), (4.1, 0), (7.2, 3)}. ANSWER: Study
Guide and Review - Chapter 4
{(2.7, −4), (3.8, −1), (4.1, 0), (7.2, 3)}
Find the inverse of each function
55. SOLUTION: -1
Write the final equation in slope-intercept form. So, f (x) =
.
ANSWER: 57. SOLUTION: Write the final equation in slope-intercept form. So,
.
ANSWER: 59. SOLUTION: eSolutions Manual - Powered by Cognero
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Write the final equation in slope-intercept form. So,
.
ANSWER: Study Guide and Review - Chapter 4
59. SOLUTION: Write the final equation in slope-intercept form. So,
.
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