Download Chapter 9 Book Review Answers

6. x + y = –1
Chapter Review
1. Determine whether the relation {(5, 3), (–5, 4), (4, 2),
(4, 1)} is a function. Explain.
ANSWER: No; The domain value 4 is paired with 2 range
values, 1 and 2.
ANSWER: Sample answer: (–1, 0), (0,–1), (1, –2), (2, –3)
Graph each equation.
7. y = –2x
ANSWER: 2. Use the table that shows the cost of gas in different
years. Is the relation a function? Explain.
ANSWER: Yes; each domain value is paired with only one range
value.
Find four solutions of each equation. Write the
solution as ordered pairs.
3. y = –5x
ANSWER: Sample answer: (–1, 5), (0, 0), (1, –5), (2, –10)
8. y = x + 5
ANSWER: 4. y = 4x
ANSWER: Sample answer: (–1, –4), (0, 0), (1, 4), (2, 8)
5. y = x + 9
ANSWER: Sample answer: (–1, 8), (0, 9), (1, 10), (2, 11)
6. x + y = –1
ANSWER: Sample answer: (–1, 0), (0,–1), (1, –2), (2, –3)
Graph each equation.
7. y = –2x
ANSWER: 9. Each small smoothie x costs $1.50, and each large
smoothie y costs $3. Find two solutions of 1.5x + 3y
= 12 to determine how many of each type Lisa can
buy with $12.
ANSWER: Sample answer: (0, 4) means she can buy 0 small
smoothies and 4 large smoothies with $12; (6, 1)
means she can buy 6 small smoothies and 1 large
smoothie with $12.
10. Find the constant rate of change between the
quantities in the table below.
ANSWER: $7.75 per hour
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8. y = x + 5
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Find the slope of the line that passes through
each pair of points.
11. F(0, 1), G(6, 4)
ANSWER: No; the ratio is different for each pair of values, and
the line does not pass through (0, 0).
ANSWER: Chapter
Review
$7.75 per hour
Find the slope of the line that passes through
each pair of points.
11. F(0, 1), G(6, 4)
ANSWER: State the slope and the y-intercept of the graph
of each equation.
17. y = 4x + 7
ANSWER: 4; 7
18. y =
12. A(–3, 7), G(5, –1)
ANSWER: –1
x
ANSWER: –
13. A lizard is crawling up a hill that rises 5 feet for
every horizontal change of 30 feet. Find the slope.
ANSWER: ;0
19. 5x + y = 0
ANSWER: –5; 0
20. –x + y = –8
The cost of renting a paddle boat varies directly
with the number of hours, as shown in the table.
ANSWER: 1; –8
21. y = –8x – 7
14. Write an equation that relates the number of hours
with the cost.
ANSWER: y = 9x
ANSWER: –8; –7
22. 4x – y = 6
15. Find the cost of renting a paddle boat for 7 hours.
ANSWER: $63
16. The temperature for one day is shown in the graph.
Determine whether the relationship between the
temperature and the time is a direct variation.
ANSWER: 4; –6
Graph each equation using the slope and yintercept.
23. y = –x + 4
ANSWER: ANSWER: No; the ratio is different for each pair of values, and
the line does not pass through (0, 0).
24. y = 2x – 6
State
the slope
and
the y-intercept
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of each equation.
17. y = 4x + 7
of the graph
ANSWER: Page 2
Chapter Review
24. y = 2x – 6
ANSWER: 27. A balloon is rising above the ground. The height in
feet y of the balloon can be given by y = 7 + 2x,
where x represents the time in seconds. State the
slope and y-intercept of the graph of the equation.
Describe what they represent.
ANSWER: Slope: 2; y-intercept: 7; the slope 2 represents the
ascent in ft per second. The y-intercept 7 represents
the initial altitude in ft before the balloon is released.
28. Jacob is ordering DVDs from a Web site. The site
charges a flat rate for shipping, no matter how many
DVDs he buys. The total cost y of Jacob’s order is
given by y = 9x + 5, where x represents the number
of DVDs he buys. State the slope and y-intercept of
the equation. Describe what they represent.
25. y =
x–3
ANSWER: ANSWER: Slope: 9; y-intercept: 5; the slope represents the cost
of each DVD ($9); the y-intercept represents the
shipping fee ($5).
Solve each system of equations by graphing.
29. y = x
y=
x–1
ANSWER: 26. y =
x+5
ANSWER: 30. y = x + 2
y = 3x
ANSWER: 27. A balloon is rising above the ground. The height in
feet y of the balloon can be given by y = 7 + 2x,
where x represents the time in seconds. State the
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slope and y-intercept of the graph of the equation.
Describe what they represent.
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Chapter Review
30. y = x + 2
y = 3x
ANSWER: ANSWER: Sample answer: y = 2x, x + y = 24; x = 8, y = 16; the
café sold 8 vanilla smoothies and 16 strawberry smoothies.
Solve each system algebraically.
35. y = 4
y = 3x – 11
ANSWER: (5, 4)
36. y = 6 – x
x = –1
ANSWER: (–1, 7)
37. –5x + y = 2
–3x + 6y = 12
ANSWER: (0, 2)
31. y = 2x + 1
x + y = –2
ANSWER: (–1, –1)
32. 5x – 3y = –3
y = –x + 1
ANSWER: (0, 1)
33. The sum of two numbers is 9, and the difference of
the numbers is 1. Write a system of equations to
represent this situation. Then solve the system to find
the numbers.
ANSWER: Sample answer: x + y = 9, x – y = 1; 5 and 4; x = 5;
y=4
34. A café sells strawberry smoothies and vanilla smoothies. On Monday, the café sold twice as many strawberry smoothies as vanilla smoothies. The total
number of smoothies sold was 24. Write a system of
equations to represent this situation. Then solve the
system and explain what the solution means.
ANSWER: Sample answer: y = 2x, x + y = 24; x = 8, y = 16; the
café sold 8 vanilla smoothies and 16 strawberry smoothies.
Solve
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35. y = 4
y = 3x – 11
38. –4x + y = 6
–5x – y = 21
ANSWER: (–3, –6)
39. 2x – 4y = 6
3x – 5y = 11
ANSWER: (7, 2)
40. 8y = 6 – 2x
x = 3 – 4y
ANSWER: infinitely many solutions
41. 7x – 3y = –4
7x = –2 + 3y
ANSWER: no solution
42. 2x + y = 3
y = –3x + 7
ANSWER: (4, –5)
43. One number subtracted from three times another
number is 11. The sum of the numbers is 1. Write
and solve a system of equations to represent this
situation. Interpret the solution.
ANSWER: 3x – y = 11; x + y = 1; (3, –2); One number is 3; the
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other number is –2.
44. Tickets to a museum cost $3 for children and $8 for
42. 2x + y = 3
y = –3x + 7
ANSWER: Chapter
Review
(4, –5)
43. One number subtracted from three times another
number is 11. The sum of the numbers is 1. Write
and solve a system of equations to represent this
situation. Interpret the solution.
ANSWER: 3x – y = 11; x + y = 1; (3, –2); One number is 3; the
other number is –2.
44. Tickets to a museum cost $3 for children and $8 for
adults. A group of four visitors to the museum spent
a total of $22 on tickets. Write and solve a system of
equations to represent this situation. Interpret the
solution.
ANSWER: x + y = 4; 3x + 8y = 22; (2, 2); There were two
children and two adults in the group.
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