ACTIVITY 9 Continued
Writing and Graphing Inequalities
Sharing Files
ACTIVITY 9
continued
3. Describe a real-world situation that can be
represented by the inequality shown in the graph.
ACTIVITY 9 PRACTICE
Answer each item. Show your work.
y
Lesson 9-1
1. Which ordered pairs are solutions of the
inequality 5y − 3x ≤ 7?
A. (0, 0)
B. (3, 5)
C. (−2, −5)
D. (1, 2.5)
E. (5, −3)
2. Apple juice costs $2 per bottle, and cranberry
juice costs $3 per bottle. Tamiko has at most $18
with which to buy drinks for a club picnic. She
lets x represent the number of bottles of apple
juice and lets y represent the number of bottles of
cranberry juice. Then she graphs the inequality
2x + 3y ≤ 18, as shown below.
y
24
20
16
12
8
4
x
4
8
4. Write an inequality for the half-plane. Is the
half-plane open or closed?
8
6
10
4
6
y
8
–10
–6
4
2
2
–10 –8 –6 –4 –2
x
2
© 2017 College Board. All rights reserved.
10
8
6
4
2
Lesson 9-2
10
© 2017 College Board. All rights reserved.
24
20
16
12
ACTIVITY PRACTICE
1. A, C, E
2. a. disagree; Tamiko can count the
integer points (x, y) in the solution
region.
b. Tamiko can look at the points (2, y)
in the solution region, where y is
an integer.
3. Possible answer: Bill wants to build a
fence for his garden. He can buy 1-foot
and 2-foot sections that lock together.
The length of the fence will be at most
24 feet. How many of each size section
can Bill buy?
4. y > 1 x − 4 ; open
5
5. y ≤ − 5 x + 5; closed
4
y
6.
4
6
8
4
6
8
10
x
–4
10
a. Tamiko states that the graph does not help her
decide how many bottles of each type of juice
to buy, because there are infinitely many
solutions. Do you agree or disagree? Why?
b. Suppose Tamiko decides to buy two bottles of
apple juice. Explain how she can use the graph
to determine the possible numbers of bottles
of cranberry juice she can buy.
2
–2
–6
y
8
–10
6
4
2
–2
2
4
6
8
10
6
10
2
6
10
10
8
6
4
2
5. Write an inequality for the half-plane. Is the
half-plane open or closed?
–10 –8 –6 –4 –2
2
x
x
y
7.
–8
–10
10
–2
–2
–4
–6
–8
–10
–6
–2
–2
–4
–6
–8
–10
x
–4
–6
–8
–10
6. Sketch a graph of the inequality
y ≥ − 2 x + 2.
5
7. Sketch a graph of the inequality 3y > 7x − 15.
Activity 9 • Writing and Graphing Inequalities
163
Activity 9 • Writing and Graphing Inequalities
163
15
25
35
8. There are at most 30 students in Mr. Moreno’s
history class.
a. Write an inequality in two variables that
represents the possible numbers of boys b and
girls g in the class.
b. Graph the inequality on a coordinate plane.
c. Explain whether your graph has a solid
boundary line or a dashed boundary line.
d. Choose a point in the shaded region of your
graph and explain what the point represents.
b
9. Tickets for the school play cost $3 for students and
$6 for adults. The drama club hopes to bring in at
least $450 in sales. The auditorium has 120 seats.
Let a represent the number of adult tickets and
s represent the number of student tickets.
a. Write an inequality in two variables that
represents the desired ticket sales.
b. Write an inequality in two variables that
represents the possible numbers of tickets that
can be sold.
c. Sketch both inequalities on the same grid.
What does the intersection of the two graphs
represent?
c. solid line; at most includes exactly
30 students
d. (10, 15): There are 10 boys and
15 girls in the class.
9. a. 3s + 6a ≥ 450
b. s + a ≤ 120
c.
a
120
108
96
84
72
60
48
36
24
12
10. When is the boundary line of the graph of an
inequality in two variables part of the solution?
Lesson 9-3
15
45
75
105 145
s
The intersection (90, 30) represents
selling 90 student tickets and
30 adult tickets.
10. When the inequality uses ≤ or ≥,
the boundary line is part of the
solution.
11.
11. Tim left school on his bike at the same time Holly
left the store. Both Tim and Holly are going to
Holly’s house. The equation d = 2 − 0.05m gives
Holly’s distance from Holly’s house after m
minutes. The equation d = 4 − m gives
5
Tim’s distance from Holly’s house after m minutes.
Sketch a graph of Holly’s and Tim’s trips on the
same coordinate plane.
12. Compare the total time for Tim’s trip to the total
time for Holly’s trip.
13. Part of Tim’s trip includes the way Holly will walk.
Use your graph to estimate when Tim will run
into Holly.
14. Kane researched the cost of a taxi ride in a nearby
city. He found conflicting information about the
per-mile cost of a ride. The graph below shows
his findings.
C
20
16
12
8
4
d
2
8
6
4
Distance (miles)
a. What can you conclude about the cost per
mile of a taxi ride?
b. How much should Kane expect to pay for a
five-mile taxi ride? Explain.
MATHEMATICAL PRACTICES
Look For and Make Use of Structure
15. Graph the inequality x < 3 on a number line and
on the coordinate plane. Describe the differences
in the graphs.
d
12
10
8
6
4
2
–20 –2
–4
–6
10
30
50
70
90
m
12. Tim took 20 minutes and Holly
took 40 minutes.
13. within the first 14 minutes
14. a. The cost is between $3 and $2
per mile after an initial cost
of $2.
b. Between $12 and $17; the cost is
between $3 and $2 per mile after
an initial cost of $2.
ADDITIONAL PRACTICE
If students need more practice on the
concepts in this activity, see the
Additional Unit Practice in Teacher
Resources on SpringBoard Digital for
additional practice problems.
164
The coordinate plane shows all
ordered pairs (x, y) with x < 3. The
number line shows all real numbers
x < 3.
y
10
8
6
4
2
–10
–10
164
SpringBoard® Integrated Mathematics I, Unit 2 • Linear Functions
15.
–6
–5
2
–2
–2
–4
–6
–8
–10
0
6
5
10
x
10
SpringBoard® Integrated Mathematics I, Unit 2 • Linear Functions
10
© 2017 College Board. All rights reserved.
40
35
30
25
20
15
10
5
© 2017 College Board. All rights reserved.
8. a. b + g ≤ 30
b.
g
5
Writing and Graphing Inequalities
Sharing Files
ACTIVITY 9
continued
Cost of Taxi Ride ($)
ACTIVITY 9 Continued