y
y
(0, 3)
5. Graph: x=2.
The graph is a vertical line with x-intercept (2,0).
12. Rate of change = 1,567,582 −1,293,953
2010 −2000
Chapter 3 Review Exercises
3. (−4,−2) is 4 units left and 2 units down. See the graph
below.
4. Point A is 5 units left and 1 unit down. The coordinates
10. We substitute 2 for xand −6 for y.
Since 10 = 10 is true, the pair (0,5) is a solution.
12. To show that a pair is a solution, we substitute, replacing x
0+3
Chapter 3 Summary and Review: Review Exercises 63
2·3−3?3
13. y=2x−5
14. y=−3
4x
15. y=−x+4
x y
16. y=3−4x,ory=−4x+3
0 3
1−1
S n 13
30
40
3
y
x
(2, 0)
17. a) When n=1,S=3
18. x−2y=6
To find the x-intercept, let y= 0. Then solve for x.
19. 5x−2y=10
y
x
20. y=3
Any ordered pair (x, 3) is a solution. The variable ymust
21. 5x−4=0
x=4
22. We can choose any two points. We consider (x1,y
1)tobe
(−3,1) and (x2,y
2)tobe(3,3).
25. We plot (−5,5) and (4,−4) and draw the line containing
those points.
26. y=−5
8x−3
27. We solve for y, obtaining an equation of the form
The slope is 1
2.
28. The graph of x=−2 is a vertical line, so the slope is not
x−10y=20
31. We solve for y, obtaining an equation of the form
x
4
6
(7, 2)(-2, 2)
x
20—6 64108—4—8—10 —2
32. 5:30 P.M. is 2.5 hr after 3:00 P.M. In this time the number
34. Rate of change = m=31.4−7.4
2011 −2001
=24
35. We substitute 0 for yand solve for x.
36. m=−8−8
(−2,−3).
A=l·w
38. a) From Telluride to Station St. Sophia, the ascent
Chapter 3 Discussion and Writing Exercises
1. With slope 5
3, for each horizontal change of 3 units, there
4. Any ordered pair (x, −2) is a solution of y=−2. All points
Chapter 3 Test
4. Point B is 0 units left or right and 4 units down. The
y
Chapter 3 Test 67
The line appears to pass through (−2,1). We check to
6. y=2x−1
−2−5
0−1
7. y=−3
2x,ory=−3
2x+0
When x=2,y=−3
8. 2x−4y=−8
2x−4y=−8
−4y=−16
9. 2x−y=3
2·0−y=3
−y=3
We let x= 3. Then
2x−y=3
10. 2x+8=0
−4 0
11. y=5
12. We can choose any two points. We consider (x1,y
1)tobe
13. We plot (−3,1) and (5,4) and draw the line containing
these points.
14. We solve for y.
2x−5y=10
15. The graph of x=−2 is a vertical line, so the slope is not
16. 3y=1
17. y=−11x+8
19. a) In 2007, t= 0, and C= 606 ·0 + 8593 = $8593.
Cumulative Review Chapters 1 – 3 69
20. The time that elapses from 2:38 to 2:40 is 2 minutes. In
21. The time that elapses from 1:00 P.M. to 5:00 P.M. is 4
22. We solve for y, obtaining an equation of the form
24. We plot the given points. We see that the other vertices
of the square are (−3,4) and (2,−1).
Cumulative Review Chapters 1 – 3
4. First we find decimal notation for 7
9=0.7, so −7
9=−0.7.
7. The reciprocal of −8
7is −7
8because −8
7−7
8=1.
11. 5
18 ÷−5
12=5
18 ·−12
5=−5·12
18 ·5=−5/ ·2·6/
3·6/ ·5/ =−2
3
15. 4
16. −8+w=w+7
17. 7.5−2x=0.5x
75=25xAdding 20x
18. 4(x+2)=4(x−2)+16
19. 2(x+2)≥5(2x+3)
20. x−5
6=1
2
21. 9x−12y=−3
4.
22. x=−15
25. A=1
27. To find the x-intercept, substitute 0 for yand solve for x.
2x−7y=21
2·0−7y=21
−7y=21
y
Cumulative Review Chapters 1 – 3 71
Find the y-intercept:
Find a third point as a check. Let x=−5.
30. Graph: y=−2.
This is the equation of a horizontal line with y-intercept
(0,−2).
31. Graph: y=−2x+1.
We see from the equation that the y-intercept is (0,1).
32. Graph: 3y+6=2x.
The x-intercept is (3,0).
When x=0,y=−3
2·0=0.
When x=2,y=−3
34. Graph: x=4.5.
y
72 Chapter 3: Graphs of Linear Equations
35. We use the points (−2,3) and (2,2) to find the slope.
36. Familiarize. Let x= the number, in millions, of Ameri-
cans with O-negative blood. Then x+94.2 = the number
x=20.2
then 20.2+94.2, or 114.4 million have O-positive blood.
Adding 20.2 and 114.4, we get 134.6 million, the number
of Americans with either O-positive or O-negative blood.
State. 20.2 million Americans have O-negative blood.
37. Familiarize. Let h= the number of hours Cory can work
7+10+9+6+h≤40
Solve.
38. Familiarize. Let w= the length of the first piece of wire.
Translate.
Length
length
length
5w= 143
Solve.
5w+ 3 = 143
14
5w= 140
39. 1000 ÷100 ·10 −10 = 10 ·10 −10 = 100 −10 = 90
40. m=−7−3
2−(−4) =−10
6=−5
3
41. 4|x|−13 = 3
4|x|=16
42. 2+5x
4=11
28 +8x+3
7,LCD = 28
43. p=2
m+Q