Download Document

LESSON
3.5
Answers for the lesson “Write and Graph
Equations of Lines”
17. y 5 4x 2 16
Skill Practice
1. The point of intersection on the
y-axis when graphing a line.
2. Sample answer: To find the
x-intercept let y 5 0 and solve for
x. To find the y-intercept let x 5 0
and solve for y.
4
3. y 5 }x 2 4
3
2
22
19. y 5 2}x 2 }
3
3
1
20. y 5 2}x 2 3
6
21. y 5 7
22. x 5 3
1
4. y 5 }x 2 2
5
23. y 5 22x 2 1
3
1
5. y 5 2}x 2 }
2
2
24. y 5 24
6
5
3
5
6. y 5 2}x 2 }
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
18. y 5 3x 2 20
3
3
7. y 5 }x 2 }
2
2
8
1
8. y 5 2}x 2 }
3
3
9. B
37
1
25. y 5 }x 1 }
5
5
26. x 5 22
5
27. y 5 2}x 2 4
2
1
28. y 5 }x 2 2
2
10. y 5 25x 2 12
29. D
11. y 5 3x 1 2
1
30. y 5 }x
9
3
4
31. y 5 2}x 1 }
7
7
12. y 5 4x 2 6
5
13. y 5 2}x
2
32. x 5 4
4
2
14. y 5 }x 2 }
9
9
1
33. y 5 }x 1 2
2
11
15. y 5 2}x 2 12
5
34. y 5 25
16. y 5 2x 2 1
5
40
35. y 5 2}x 2 }
3
3
Geometry
Answer Transparencies for Checking Homework
79
36.
40.
y
1
1
y
x
2
(21, 21)
(0, 1)
(5, 1)
21
x
(0, 25)
37.
2
1
(0, 1)
(1, 0)
21
38.
y
41.
y
21
x
x
(1, 22)
(0, 23)
y
(0, 8)
y
42.
1
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
(27, 0)
21
(21, 4)
(27, 24)
1
21
39.
x
x
43.
y
y
1
21
x
(21, 3)
(1, 2)
1
(3, 22)
(0, 23)
21
x
Geometry
Answer Transparencies for Checking Homework
80
y
44.
53.
y
(0, 9)
(0, 2)
1
(21, 5)
(1, 21)
21
x
2
(0, 21)
21
(21, 25)
45. Sample: The student replaced the
wrong variable with 0 to find each
no solutions
intercept. To find the x-intercept,
54.
let y 5 0, 5x 2 3(0) 5 215,
y
x 5 23, (23, 0). To find the
(1, 4)
y-intercept, let x 5 0,
5(0) 2 3y 5 215, y 5 5, (0, 5).
2
46. (0, 1); y 5 2x 1 1
x
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
(6, 26)
(5, 28)
48. (3, 0); y 5 1.5x 2 4.5
49. 4, 4; y 5 2x 1 4
1
1
52. (2, 0); 0, 2}
2
(4, 0)
21
47. (21, 21); y 5 2x 2 2
5
50. 22, 25; y 5 2}x 2 5
2
1
51. 220, 10; y 5 }x 1 10
2
x
one solutions
55.
y
(0, 6)
2
1
(1, 1)
21
x
infinitely many solutions
Geometry
Answer Transparencies for Checking Homework
81
answer: If a false equation
occurs the lines are parallel. If the
variables drop out, a true equation
occurs and the lines are the same
line. If a point is found the lines
intersect at that point.
57. 4
58. 5
59. S(22, 3)
62. a. y 5 50, y 5 4x
b.
Cost of going to the park
(dollars)
56. Check students’ work. Sample
y
60
50
40
30
20
10
0
y
0
10
20
30
x
Number of visits
c. 13 visits ; Sample answer: The
22
x
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
R(27, 23)
T(10, 27)
Check the slopes of each line
segment. If two of the slopes
are negative reciprocals of
one another the lines are
perpendicular and form a
right angle.
Problem Solving
60. y 5 23x 1 50; slope: the monthly
charge, y-intercept: initial
one-time charge $326
point of intersection is
(12.5, 50). Using the graph
you can see that for 13 or more
visits in a year the cost of going to the park is lower if you
buy a yearly pass than if you
pay the $4 entrance fee each
time you visit.
63. 2x 1 3y 5 24; A: cost of a small
slice, B: cost of a large slice, C:
amount of money you can spend.
y
64. No;
Distance (mi)
1
2
your friend
1
0
you
0
10
20
30
40 x
Time (min)
61. y 5 2.1x 1 2000; slope: gain in
weight per day, y-intercept:
starting weight before the
growth spurt
Geometry
Answer Transparencies for Checking Homework
82
65. a. 2b 1 c 5 13, 5b 1 2c 5 27.50
Price of a
package of clasps
b.
c
14
12
5b 2c 27.50
10
8
6
4
2
0
2b c 13
0 1 2 3 4 5 6 7 8 9 b
Price of a bag of beads
c. The intersection represents the
price of one bag of beads and
the price of one package of
clasps.
66. First gym: y 5 31x 1 50,
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
second gym: y 5 20x 1 42;
8 302
, } ; second gym:
1 2}
11 11 2
it has a lower initial cost and a
lower monthly cost.
Geometry
Answer Transparencies for Checking Homework
83