5-6 Graphing Inequalities in Two Variables
Graph each inequality.
18. 5x + y > 10
ANSWER: 19. 2x + y < −3
ANSWER: 20. −2x + y ≥ −4
ANSWER: 21. 8x + y ≤ 6
ANSWER: 22. 10x + 2y ≤ 14
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5-6 Graphing Inequalities in Two Variables
22. 10x + 2y ≤ 14
ANSWER: 23. −24x + 8y ≥ −48
ANSWER: 30. DECORATING Sybrina is decorating her bedroom. She has $300 to spend on paint and bed linens. A gallon of
paint costs $14, while a set of bed linens costs $60.
a. Write an inequality for this situation.
b. How many gallons of paint and bed linen sets can Sybrina buy and stay within her budget?
ANSWER: a. 14x + 60y ≤ 300
b. Sample answer: 5 gallons of paint and 3 bed linen sets
37. SOCCER The girls’ soccer team wants to raise $2000 to buy new goals. How many of each item must they sell to
buy the goals?
a. Write an inequality that represents this situation.
b. Graph this inequality.
c. Make a table of values that shows at least five possible solutions.
d. Plot the solutions from part c.
ANSWER: a. x + 1.25y ≥ 2000
b.
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b. How many gallons of paint and bed linen sets can Sybrina buy and stay within her budget?
ANSWER: a. 14x + 60y ≤ 300
5-6 Graphing
Inequalities in Two Variables
b. Sample answer: 5 gallons of paint and 3 bed linen sets
37. SOCCER The girls’ soccer team wants to raise $2000 to buy new goals. How many of each item must they sell to
buy the goals?
a. Write an inequality that represents this situation.
b. Graph this inequality.
c. Make a table of values that shows at least five possible solutions.
d. Plot the solutions from part c.
ANSWER: a. x + 1.25y ≥ 2000
b.
c. Sample answer: (400, 1600), (200,1500), (300, 1400), (400, 1300), (1000, 1000)
d. Sample points should be in the shaded region of the graph in part b.
46. ERROR ANALYSIS Reiko and Kristin are solving
by graphing. Is either of them correct? Explain your
reasoning.
ANSWER: Reiko; Kristin used a test point located on the line and shaded the incorrect half-plane.
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CHALLENGE
47. Write a linear inequality for which (–1, 2), (1, 1), and (3, –4) are solutions but (0, 1) is not.
ANSWER: Page 3
5-6 Graphing
Inequalities in Two Variables
ANSWER: Reiko; Kristin used a test point located on the line and shaded the incorrect half-plane.
47. CHALLENGE Write a linear inequality for which (–1, 2), (1, 1), and (3, –4) are solutions but (0, 1) is not.
ANSWER: Sample answer:
51. What is the domain of this function?
A {x | 0 ≤ x ≤ 3}
B {x | 0 ≤ x ≤ 9}
C {y | 0 ≤ y ≤ 9}
D {y | 0 ≤ y ≤ 3}
ANSWER: B
52. EXTENDED RESPONSE An arboretum will close for the winter when all of the trees have lost their leaves. The
table shows the number of trees each day that still have leaves.
a. Write an equation that represents the number of trees with leaves y after d days.
b. Find the y-intercept. What does it mean in the context of this problem?
c. After how many days will the arboretum close? Explain how you got your answer.
ANSWER: a. y = 390 − 13d
b. 390; the y–intercept represents the number of trees with leaves in the arboretum on day 0.
c. The arboretum will close after 30 days. I found the solution of 0 = 390 – 13d.
53. Which inequality best represents the statement below?
A jar contains 832 gumballs. Ebony’s guess was within 46 pieces.
F |g − 832| ≤ 46
G |g + 832| ≤ 46
H |g − 832| ≥ 46
J |g + 832| ≥ 46
ANSWER: F
3
54. GEOMETRY If the rectangular prism has a volume of 10,080 cm , what is the value of x?
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H |g − 832| ≥ 46
J |g + 832| ≥ 46
ANSWER: 5-6 Graphing
Inequalities in Two Variables
F
3
54. GEOMETRY If the rectangular prism has a volume of 10,080 cm , what is the value of x?
A 12
B 14
C 16
D 18
ANSWER: D
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