⫺5
4
3
(1, 4)
3x y 7
Chapter 3
Graphs of Linear Equations
Exercise Set 3.1
RC2. The statement is false. A point that lies on an axis is
RC4. True
4. IV
16. Negative
30. 5x−3y=15
32. 2p−3q=−13
2(−5) −3·1?−13
−13
TRUE
34. y=x+3
y=x+3
36. To show that a pair is a solution, we substitute, replacing x
5
y
y
3
4
5
5
(3, -8)
axis
4
⫺
3
⫺
2
5
(4, 3)
(0, ⫺1)(⫺1, ⫺2)
(⫺2, ⫺3)
50 Chapter 3: Graphs of Linear Equations
The line appears to pass through (1,4) also. We check to
38. 6x−3y=3
(3,5) appears to be another solution. We check.
40. 8−4(q+2)= −7
42. −3
44. 2b−5+b=6(b−1)
46.
54.
2
-2
-6
-8
-10
y
⫺5
y
⫺2
y
⫺5
y
⫺2
⫺3
⫺1
y
4
5
y
58.
Exercise Set 3.2
RC2. 5y−2x=0
RC4. 5x−2y=−5
2. x y
4. x y
6. x y
8. x y
10. x y
−3−5
14. x+y=4
x y
y
⫺4⫺224
⫺5⫺3⫺1135
1
x
y
⫺4
⫺5
y
⫺2
⫺3
⫺1
52 Chapter 3: Graphs of Linear Equations
16. x y
18. x+2y=−6
x y
2−4
20. x y
24. 6y+2x=8
26. a) In 2002, P= 426 ·0+25,710 = $25,710.
b)
28. a) T=−2.15(1) + 54 = 51.85◦
c) Solve: −4=−2.15m+54
4
5
x 2y 2
⫺
4
⫺
224
⫺
5
⫺
3
⫺
1135
⫺
1
x
30. 4.89
42. −420
Exercise Set 3.3
RC6. The graph of x= 4 is a vertical line with (4,0) as its
y=10
10. −2x+3y=7
(b) Solve: −2x=7
14. To find the y-intercept, let x= 0 and solve for y.
The y-intercept is (0,1).
To find the x-intercept, let y= 0 and solve for x.
16. To find the y-intercept, let x= 0 and solve for y.
4
y
5
y
5x 10 5y
5
y
4
5
2x 6y 12
18. To find the y-intercept, let x= 0 and solve for y.
y=6
20. To find the y-intercept, let x= 0 and solve for y.
3y−6=0
3y=6
3,0).
22. To find the y-intercept, let x= 0 and solve for y.
The x-intercept is (2,0).
24. To find the y-intercept, let x= 0 and solve for y.
26. To find the y-intercept, let x= 0 and solve for y.
6y=12
28. To find the y-intercept, let x= 0 and solve for y.
−1=y
⫺4⫺224
⫺5⫺3⫺1135
⫺1
x
2
3
2
3
Exercise Set 3.3 55
30. To find the y-intercept, let x= 0 and solve for y.
2x−1=0
2x=1
32. To find the y-intercept, let x= 0 and solve for y.
x=3
34. To find the y-intercept, let x= 0 and solve for y.
36. To find the y-intercept, let x= 0 and solve for y.
0=6y−2
38. To find the y-intercept, let x= 0 and solve for y.
y
4
3
5
y
y
y
⫺4
⫺2
⫺3
⫺4
⫺5
⫺3
⫺4⫺224
⫺5⫺3⫺1135
⫺1
1
x
8
10
y
40.
42.
44.
46.
50. 12y=45
56. x=−1
62. 1
64. Substitute 2 for xand 0 for y.
0=m·2+6
66. Substitute 0 for xand −8 for y.
Chapter 3 Mid-Chapter Review
1. In Quadrant II, all first coordinates are negative and all
second coordinates are positive. Since any negative num-
2. We substitute 0 for xand solve for y.
3. True; when x= 0, we have y=C
B.
7. Point A is 1 unit left and 0 units up or down. Its coordi-
nates are (−1,0).
8. Point F is 0 units left or right and 3 units down. Its coor-
dinates are (0,−3).
9. −2q−7p=19
−2(−5) −7·8?19
−1,2
3is a solution.
11. To find the x-intercept, let y= 0. Then solve for x.
−3x=18
−3·0+2y=18
2y=18
x−1
2=0
−1
2=10y
y
13. To find the x-intercept, let y= 0. Then solve for x.
x−40 = 20y
14. To find the x-intercept, let y= 0. Then solve for x.
1
3y−5
6x=35
To find the y-intercept, let x= 0. Then solve for y.
15. Graph: −2x+y=−3.
x=3
A third point is (1,−1). We plot this point and the inter-
cepts and draw the line.
This is an equation of the form y=bwith b=−3
2.
Its graph is a horizontal line with y-intercept (0,b), or
0,−3
17. Graph: y=−x+4.
18. Graph: x=0.
y
2
3
⫺3
(⫺5, ⫺2)
4
⫺4
⫺2
⫺3
3
(4, ⫺3)
(⫺3, 5)
19. y=−1,ory=0·x−1
20. x=1
21. y=−x−1
22. y=x−1
23. y=x+1
The slope is 1 so either A or E is the correct choice. We
25. Most would probably say that the second equation would
26. A= 0. If the line is horizontal, then regardless of the value
27. Any ordered pair (7,y) is a solution of x= 7. Thus, all
Exercise Set 3.4
RC6. The change in yis called rise. The correct answer is
6. We can use any two ordered pairs. We choose (−2,4) and
4−(−2) =−3
6=−1
2
m=2−(−4)
−3−2=6
−5=−6
5
⫺4⫺224
⫺5⫺3⫺1135
1
x
y
16.
24. m=−0.04 −2.4
0.2−0.2=−2.44
0
The slope is not defined.
28. y=−3
5x+28
32. x−4y=8
34. 2x−4y=8
36. y=−1
3=0·x−1
3
40. 4y=9x−7
4.
42. 16+2x−8y=0
44. x=−3
46. 3x−1
48. −x=2
11y
50. m=148.8
2400 =0.062=6.2%
56. Rate of change = 15,876 −37,775
60. Rate of change = 29.2−16.7
64. t−6+4t+5=5t−1
⫺4
4
(0, 4)
⫺
2
⫺
4
2
⫺
442
(2, 0)
(0, ⫺4)
Chapter 3 Summary and Review: Study Guide 61
Chapter 3 Vocabulary Reinforcement
5. The graph of x=ais a vertical line. The x-intercept is
Chapter 3 Concept Reinforcement
5. Ax +By =C
Chapter 3 Study Guide
2. x+2y=8
2y=−x+8
3. To find the x-intercept, we let y= 0 and solve for x.
We find a third point as a check. Let x=4.