Name ________________________________________ Date __________________ Class__________________
LESSON
2-5
Reteach
Linear Inequalities in Two Variables
Graphing a linear inequality is similar to graphing a linear function.
Graph y ≤
Step 1
2
x + 1 using the slope-intercept form.
3
Write the corresponding equation. Then identify the slope and the y-intercept.
y=
2
x +1
3
2
and b = 1
3
m=
Step 2
Draw the graph of y =
2
x + 1.
3
Draw a solid boundary line for ≤ or ≥.
Draw a dashed boundary line for < or >.
Step 3
Shade the half-plane below the line for
< or ≤. Shade the half-plane above the
line for > or ≥.
Step 4
Check using a point in the shaded
region. Use (0, 0).
y≤
2
x +1
3
? 2
0 ≤ (0) + 1
3
?
0 ≤ 19
Graph each inequality.
1. y ≤ x + 2
a. m = _______________
b. b = _______________
c. boundary line is _______________
d. shade half-plane _______________ the line
2. y > −2x + 1
a. m = _______________
b. b = _______________
c. boundary line is _______________
d. shade half-plane _______________ the line
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2-38
Holt Algebra 2
Name ________________________________________ Date __________________ Class__________________
LESSON
2-5
Reteach
Linear Inequalities in Two Variables (continued)
The intercepts can be used to graph a linear inequality.
Graph 2x + y > 4 using the intercepts.
Step 1
Write the corresponding equation. Then identify the x-intercept and the y-intercept.
2x + y = 4.
When y = 0, x = 2; plot (2, 0).
When x = 0, y = 4; plot (0, 4).
Step 2
Draw the graph of 2x + y = 4 using a
dashed line.
Step 3
Choose a point to check which half-plane
to shade. Use (0, 0).
2x + y > 4
?
2 (0) + (0) > 4
?
0 > 4×
Step 4
The inequality is false, so shade the half-plane above the line.
Graph each inequality.
3. 2x + 4y > 8
4. −3x + y ≤ −1
a. x-intercept _______________
a. x-intercept _______________
b. y-intercept _______________
b. y-intercept _______________
c. boundary line _______________
c. boundary line _______________
d. test (0, 0) _______________
d. test (0, 0) _______________
e. shade _______________ the line
e. shade _______________ the line
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2-39
Holt Algebra 2
Practice B
Practice C
1. a. 25x + 35y ≥ 2400
1.
b. 61 tickets
2. a. 15x + 10.75y ≤ 137.25
b. 4 ≤ x ≤ 7; 3 ≤ y ≤ 6
c. Possible answer: Depending on when
you start the 10-day period, the
number of weekdays and weekend
days will vary.
2.
d. Possible answer: Pick up the car on a
Friday and return it the following
Sunday. This gives you 6 weekend
days at the lower rate and 4 weekdays
at the higher rate.
3. y ≥ 2x − 6
3.
5. y >
1
4. y < − x + 2
3
3
x −3
4
Reteach
1. a. 1
b. 2
c. Solid
d. Below
4.
5. a. 2 x +
5y
≥ 250
3
2. a. −2
b. 60 tickets
b. 1
c. Dashed
d. Above
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A20
Holt Algebra 2
R where the domain is limited to x < 12
are in the shaded half-plane and
therefore in the solution region.
3. a. 4
b. 2
c. Dashed
Problem Solving
d. False
1. 12n + 8.5p ≤ 200
e. Above
2. 16.7; 23.5
3.
4. Positive whole numbers
4. a.
5. Solid, because the total cost could be
equal to $200
1
3
6. The solution region is the area below the
line, because they cannot spend any
more than $200.
7. No; Possible answer: because the point
(10, 15) is not in the shaded region of the
graph, so it is not a solution.
b. −1
c. Solid
d. False
e. Below
8. 13
10. D
9. 9 of each type.
11. A
Reading Strategies
1. a. y ≥ x + 1
b. Possible answer: (0, 6) and (−4, 4)
c. Yes
2. y > x + 1
3. Change the solid boundary line to a
dashed line.
1. Yes; point J lies in the solution region.
4. The boundary line and the shaded area
below it
2. Yes; point K lies in the solution region.
5. y < x + 1
Challenge
3. y = −
1
x
2
6. y ≤ x + 1
LESSON 2-6
Practice A
4. Yes; all points on the line segment JK lie
in the solution region.
1. 3
5. −4 ≤ x ≤ 4
⎛ 1 ⎞
6. a. 3 x + 4 ⎜ − x ⎟ < 12, x < 12
⎝ 2 ⎠
3.
1
f (x)
4
⎛1 ⎞
2. f ⎜ x ⎟
⎝4 ⎠
4. f(x + 5)
b. Possible answer: All the points on line
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A21
Holt Algebra 2