unit 6 review for final
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Determine the slope of this line segment.
y
4
A
2
–4
–2
2
0
–2
4
x
B
–4
a.
b.
____
c.
2
3
3
2
d.
2. Which line segment has slope
2
3
3
2
7
?
4
i)
ii)
y
4
y
4
A
2
2
A
–4
–2
0
2
4
–4
x
–2
–2
–2
B
B
–4
iii)
0
–4
iv)
2
4
x
y
y
A
4
4
2
2
B
–4
–2
0
2
4
–4
x
–2
–2
–2
B
A
–4
–4
a. iii
b. ii
____
c. i
d. iv
3. Determine the slope of the line that passes through G(3, –3) and H(–5, 9).
a.
b.
____
0
c.
3
2
d.
2
3
2
3
3
2
4. Is the slope of this line segment positive, negative, zero, or not defined?
y
8
S
4
–8
–4
0
4
8
x
–4
T
–8
a. zero
b. positive
____
c. not defined
d. negative
5. Is the slope of this line segment positive, negative, zero, or not defined?
2
4
x
y
8
4
–8
–4
0
4
8
x
–4
R
S
–8
a. positive
b. negative
____
c. zero
d. not defined
6. Is the slope of this line segment positive, negative, zero, or not defined?
y
8
B
4
–8
–4
0
4
8
C
x
–4
–8
a. negative
b. not defined
____
c. positive
d. zero
7. Is the slope of this line segment positive, negative, zero, or not defined?
y
8
V
4
–8
–4
W
0
4
8
x
–4
–8
a. positive
b. negative
____
c. not defined
d. zero
8. Determine the steepness of this roof by calculating its slope.
rise
run
a.
b.
____
5
3
5
3
c.
d.
3
5
3
5
9. A straight section of an Olympic downhill ski course is 34 m long. It drops 16 m in height. Determine the
slope of this part of the course.
a.
c.
b.
____ 10. Which of these line segments are parallel?
d.
y
4
B
D
2
A
–4
–2
0
2
F
4
x
–2
C
H
–4
E
G
a. CD and EF
b. EF and GH
c. AB and CD
d. AB and EF
____ 11. Determine the slope of the line that is perpendicular to this line segment.
y
4
2
–4
–2
0
B
2
4
x
–2
A –4
a. 3
c.
1
3
b. –3
d.
–
1
3
____ 12. Determine the slope of the line that is parallel to this line segment.
y
4
2
X
–4
K
–2
0
2
4
x
–2
–4
a.
–
b.
7
3
3
7
c.
3
7
d.
–
7
3
____ 13. Determine the slope of a line that is perpendicular to the line through W(–9, 7) and X(6, –10).
a.
c. –15
15
17
b.
d. 15
17
15
17
____ 14. Determine the slope of a line that is parallel to the line through L(–6, 3) and K(12, –9).
a. 2
c.
2
3
3
b. 3
d.
3
2
2
____ 15. A line has x-intercept –5 and y-intercept 1. Determine the slope of a line parallel to this line.
a. –5
c. 5
b.
d. 1
1
–
5
5
____ 16. A line has x-intercept 4 and y-intercept –5. Determine the slope of a line perpendicular to this line.
a.
c. 5
4
5
4
b.
d. 4
5
4
5
____ 17. The slope of this line is
. What is the equation of the line?
y
4
2
–4
–2
0
2
4
x
–2
–4
a.
c.
y=
b. y =
d.
y=
y=x
____ 18. Predict what will be common about the graphs of these equations.
i) y = 3x + 6
iii) y = 3x – 6
ii) y = 3x – 5
iv) y = 3x + 5
a. All the graphs will have the same slope.
c. All the graphs will have the same
y-intercept.
b. All the graphs will have the same
d. None of the above.
x-intercept.
____ 19. Predict what will be common about the graphs of these equations.
i) y = 2x – 6
iii) y = – 5x – 6
ii) y = –3x – 6
iv) y = 5x – 6
a. All the graphs will have the same
y-intercept.
b. All the graphs will have the same
x-intercept.
____ 20. The slope of this line is
c. All the graphs will have the same slope.
d. None of the above.
. What is the equation of the line?
8
y
6
4
2
–4
–2
0
2
4
x
–2
–4
–6
–8
a.
c.
b.
d.
____ 21. Write an equation for the graph of a linear function that has slope
a.
c.
b.
d.
____ 22. Which graph represents the equation
a.
?
c.
and y-intercept –3.
y
–4
4
4
2
2
0
–2
y
2
4
–4
x
–2
0
–2
–2
–4
–4
b.
4
x
2
4
x
d.
y
–4
4
4
2
2
0
–2
y
2
4
–4
x
–4
–4
4
2
–2
0
0
–2
y
–4
–2
–2
____ 23. Write an equation to describe this graph.
2
4
x
–2
–4
a.
2
c.
b.
d.
____ 24. For a service call, a plumber charges a $95 initial fee, plus $45 for each hour he works. Write an equation to
represent the total cost, C dollars, for t hours of work.
a.
c.
b.
d.
____ 25. To join a tennis club, Josephine pays a start-up fee of $130, plus a monthly fee of $24. Write an equation to
represent the total cost, C dollars, for t months of membership.
a.
c.
b.
d.
____ 26. Which graph has slope 1 and y-intercept 0?
a.
c.
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
b.
2
4
x
2
4
x
d.
y
–4
–2
y
4
4
2
2
0
2
4
x
–4
–2
0
–2
–2
–4
–4
____ 27. Write an equation to describe this graph.
d
20
10
–20
–10
0
10
20
t
–10
–20
a.
b.
c.
d.
____ 28. Write an equation to describe this graph.
y
12
6
–12
–6
0
6
12
x
–6
–12
a.
c.
b.
d.
____ 29. Write an equation for the graph of a linear function that has slope 1 and y-intercept 8.
a.
b.
c.
d.
____ 30. Determine the slope and y-intercept of the graph of this equation:
a.
slope:
; y-intercept: 9
c. slope:
; y-intercept: 2
b.
d.
slope: 9; y-intercept:
slope:
; y-intercept: 3
____ 31. Determine the slope and y-intercept of this graph.
y
4
2
–4
0
–2
2
4
x
–2
–4
a.
b.
slope:
slope:
c.
; y-intercept: –1.5
d.
; y-intercept: 1.5
____ 32. Which equations represent parallel lines?
a.
,
b.
,
slope:
; y-intercept: 1.5
slope:
; y-intercept: –1.5
c.
d.
,
,
____ 33. Which equations represent perpendicular lines?
a.
c.
,
b.
,
,
d.
,
____ 34. Describe the graph of the linear function with this equation:
a.
b.
c.
d.
The graph is a line through (–2, 3) with slope
.
The graph is a line through (2,
) with slope
.
The graph is a line through (2,
) with slope
.
The graph is a line through (–2, 3) with slope
.
____ 35. Write an equation for the graph of a linear function that has slope 8 and passes through R(4,
a.
b.
).
c.
d.
____ 36. Describe the graph of the linear function with this equation:
a. The graph is a line through (8, –7) with slope .
b. The graph is a line through ( , 7) with slope .
c. The graph is a line through ( , 7) with slope 5.
d. The graph is a line through (8, –7) with slope 5.
____ 37. Which graph represents the equation
?
a.
c.
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
b.
2
4
x
2
4
x
d.
y
–4
–2
y
4
4
2
2
0
2
4
x
–4
–2
0
–2
–2
–4
–4
____ 38. Write an equation in slope-point form for this line.
y
4
2
–4
0
–2
2
4
x
–2
–4
a.
c.
b.
d.
____ 39. Write this equation in slope-intercept form:
a.
b.
13
5
13
5
c.
d.
13
5
13
5
____ 40. Write this equation in slope-intercept form:
a.
c.
b.
d.
____ 41. Determine the y-intercept of the graph of this equation:
a. 3
c. 23
b.
d.
____ 42. Determine the y-intercept of the graph of this equation:
a.
c.
b. 13
d. 3
____ 43. Write an equation in slope-point form for the line that passes through A(–2, 4) and
B(–9, 6).
a.
c.
b.
d.
____ 44. Write an equation in slope-point form for the line that passes through A(1, 4) and B(6, 8).
a.
c.
b.
d.
____ 45. Write an equation for the line that passes through T(–3, 3) and is parallel to the line
.
a.
c.
b.
d.
____ 46. Write an equation for the line that passes through U(3, –7) and is perpendicular to the line
.
a.
c.
b.
d.
____ 47. In which form is the equation
a. Standard form
b. Slope-intercept form
____ 48. Write this equation in general form:
a.
b.
written?
c. General form
d. Slope-point form
c.
d.
____ 49. Write this equation in general form:
a.
b.
c.
d.
____ 50. Write this equation in general form:
a.
b.
c.
d.
____ 51. Determine the x-intercept and the y-intercept for the graph of this equation:
a. x-intercept: 18; y-intercept: 12
c. x-intercept: 18; y-intercept:
b. x-intercept:
; y-intercept:
d. x-intercept:
; y-intercept: 12
____ 52. Which equation is written in general form?
a.
b.
c.
d.
____ 53. Which graph represents the equation
a.
c.
?
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
b.
2
4
x
2
4
x
d.
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
____ 54. Determine the slope of the line with this equation:
a.
c. 7
7
–
3
3
b. 3
d.
3
–
7
7
____ 55. Determine the slope of the line with this equation:
a. –4
c.
b.
____ 56. Write this equation in slope-intercept form:
a.
10
4
y=
x+
3
3
b.
10
4
y=– x+
3
3
____ 57. Which graph represents the equation
a.
d. 4
c.
10
4
x–
3
3
d.
10
y=– x–4
3
y=
?
c.
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
b.
2
4
x
2
4
x
d.
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
____ 58. Which equation is equivalent to
a.
b.
?
c.
d.
Short Answer
59. A school plans to build a wheelchair ramp from the sidewalk to the front entrance of the school. The slope of
3
the ramp must be
. The entrance to the school is 75 cm above the ground. What is the horizontal distance
32
needed for the ramp?
60. Graph the line with y-intercept 3 and slope –2.
61. The total cost for a cheese of the month club is a flat fee of $15, plus $9.50 per month. Write an equation to
represent the total cost, C dollars, for m months of membership.
62. Write this equation in slope-intercept form:
63. Write an equation for the line that passes through E(–3, –7) and F(2, 10). Write the equation in slope-point
form and in slope-intercept form.
64. Write this equation in general form:
65. Write this equation in general form:
66. Determine the slope of the line of this equation:
Problem
67. A guy wire helps to support a tower. One end of the wire is 25 m from the base of the tower. The wire has a
8
slope of . How high up the tower does the wire reach?
5
68. a) Determine the rise, run, and slope of this line segment.
y
4
A
2
–4
–2
0
2
4
x
–2
–4
B
b) Draw a line segment whose slope is:
i) zero
ii) not defined
iii) the same as the slope of the line segment in part a
69. A line passes through R(6, 9) and K(–6, 15).
a) What is the slope of line RK?
b) Line VB is parallel to RK. What is the slope of VB? Explain your answer.
c) Line WX is perpendicular to RK. What is the slope of WX? Explain your answer.
70. Describe the graph of the linear function whose equation is
.
Draw this graph without using technology.
71. A student said that the equation of this graph is
a) What mistakes did the student make?
b) What is the equation of the graph?
.
y
4
2
–4
0
–2
2
4
x
–2
–4
72. Write an equation to describe this function. Verify the equation.
y
4
2
–4
–2
0
2
4
x
–2
–4
73. Identify the graph below that corresponds to each given slope and y-intercept.
a) slope
; y-intercept 0
b) slope ; y-intercept
c) slope 4; y-intercept 0
d) slope
Graph A
; y-intercept 0
Graph B
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
Graph C
2
4
x
2
4
x
Graph D
y
–4
–2
y
4
4
2
2
0
2
4
–4
x
–2
0
–2
–2
–4
–4
74. a) Write an equation in slope-point form for this line.
y
4
2
–4
–2
0
2
4
x
–2
–4
b) Write the equation in part a in slope-intercept form. What is the y-intercept of this line?
75. Determine the slope of a line that is perpendicular to the line with this equation:
76. Write an equation in general form for the line that passes through A(3, –4) and B(11, 8).
77. Charles’s Gas Law states that the volume, v, of a fixed mass of gas at a constant pressure varies directly with
its absolute temperature, t. At 27°C, the volume of a certain amount of air is 500 mL. When the air is heated
to 90°C, the volume increases to 605 mL.
a) Write an equation in general form for this relation.
b) Determine the volume of the air when its temperature is 60°C.
c) Determine the temperature of the air when its volume is 1010 mL.
78. Graph this equation:
Describe the strategies you used.
y
8
4
–16
–12
–8
–4
0
–4
–8
4
8
12
16
x
unit 6 review for final
Answer Section
MULTIPLE CHOICE
1. ANS:
LOC:
2. ANS:
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3. ANS:
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4. ANS:
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5. ANS:
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6. ANS:
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18. ANS:
B
PTS: 1
DIF: Easy
REF: 6.1 Slope of a Line
10.RF5
TOP: Relations and Functions
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
REF: 6.1 Slope of a Line
10.RF5
TOP: Relations and Functions
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
REF: 6.1 Slope of a Line
10.RF5
TOP: Relations and Functions
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
REF: 6.1 Slope of a Line
10.RF5
TOP: Relations and Functions
KEY: Conceptual Understanding
C
PTS: 1
DIF: Easy
REF: 6.1 Slope of a Line
10.RF5
TOP: Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
REF: 6.1 Slope of a Line
10.RF5
TOP: Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
REF: 6.1 Slope of a Line
10.RF5
TOP: Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
REF: 6.1 Slope of a Line
10.RF5
TOP: Relations and Functions
KEY: Procedural Knowledge
B
PTS: 1
DIF: Moderate
REF: 6.1 Slope of a Line
10.RF5
TOP: Relations and Functions
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
6.2 Slopes of Parallel and Perpendicular Lines
LOC: 10.RF3
Relations and Functions
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
6.2 Slopes of Parallel and Perpendicular Lines
LOC: 10.RF3
Relations and Functions
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
6.2 Slopes of Parallel and Perpendicular Lines
LOC: 10.RF3
Relations and Functions
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
6.2 Slopes of Parallel and Perpendicular Lines
LOC: 10.RF3
Relations and Functions
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
6.2 Slopes of Parallel and Perpendicular Lines
LOC: 10.RF3
Relations and Functions
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
6.2 Slopes of Parallel and Perpendicular Lines
LOC: 10.RF3
Relations and Functions
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
6.2 Slopes of Parallel and Perpendicular Lines
LOC: 10.RF3
Relations and Functions
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
6.3 Investigating Graphs of Linear Functions
LOC: 10.RF7
Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
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32.
33.
34.
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6.3 Investigating Graphs of Linear Functions
LOC: 10.RF7
Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
6.3 Investigating Graphs of Linear Functions
LOC: 10.RF7
Relations and Functions
KEY: Conceptual Understanding
D
PTS: 1
DIF: Easy
6.3 Investigating Graphs of Linear Functions
LOC: 10.RF7
Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
C
PTS: 1
DIF: Easy
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
D
PTS: 1
DIF: Easy
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
D
PTS: 1
DIF: Moderate
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Moderate
6.4 Slope-Intercept Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
6.5 Slope-Point Form of the Equation for a Linear Function
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REF:
LOC:
KEY:
46. ANS:
REF:
LOC:
KEY:
47. ANS:
REF:
TOP:
48. ANS:
REF:
10.RF6
TOP: Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Easy
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
KEY: Conceptual Understanding
C
PTS: 1
DIF: Easy
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
A
PTS: 1
DIF: Easy
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Moderate
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
KEY: Conceptual Understanding
B
PTS: 1
DIF: Moderate
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
KEY: Conceptual Understanding
C
PTS: 1
DIF: Easy
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
B
PTS: 1
DIF: Easy
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
C
PTS: 1
DIF: Easy
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
C
PTS: 1
DIF: Easy
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
D
PTS: 1
DIF: Moderate
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
C
PTS: 1
DIF: Moderate
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF6
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
C
PTS: 1
DIF: Easy
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
Relations and Functions
KEY: Conceptual Understanding
C
PTS: 1
DIF: Easy
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
TOP:
49. ANS:
REF:
TOP:
50. ANS:
REF:
TOP:
51. ANS:
REF:
TOP:
52. ANS:
REF:
TOP:
53. ANS:
REF:
TOP:
54. ANS:
REF:
TOP:
55. ANS:
REF:
TOP:
56. ANS:
REF:
TOP:
57. ANS:
REF:
TOP:
58. ANS:
REF:
TOP:
Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
Relations and Functions
KEY: Conceptual Understanding
C
PTS: 1
DIF: Easy
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
Relations and Functions
KEY: Conceptual Understanding
D
PTS: 1
DIF: Easy
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
Relations and Functions
KEY: Conceptual Understanding | Procedural Knowledge
B
PTS: 1
DIF: Easy
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
Relations and Functions
KEY: Conceptual Understanding
C
PTS: 1
DIF: Easy
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
Relations and Functions
KEY: Conceptual Understanding | Procedural Knowledge
A
PTS: 1
DIF: Easy
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
Relations and Functions
KEY: Conceptual Understanding | Procedural Knowledge
D
PTS: 1
DIF: Easy
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
Relations and Functions
KEY: Conceptual Understanding | Procedural Knowledge
B
PTS: 1
DIF: Easy
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
Relations and Functions
KEY: Conceptual Understanding
A
PTS: 1
DIF: Easy
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
Relations and Functions
KEY: Conceptual Understanding | Procedural Knowledge
C
PTS: 1
DIF: Moderate
6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF6
Relations and Functions
KEY: Conceptual Understanding
SHORT ANSWER
59. ANS:
800 cm, or 8 m
PTS: 1
LOC: 10.RF5
60. ANS:
DIF: Moderate
REF: 6.1 Slope of a Line
TOP: Relations and Functions
KEY: Procedural Knowledge
y
4
2
–4
–2
0
2
4
x
–2
–4
PTS: 1
DIF: Easy
REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function
LOC: 10.RF6
TOP: Relations and Functions
KEY: Procedural Knowledge
61. ANS:
PTS: 1
DIF: Easy
REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function
LOC: 10.RF6
TOP: Relations and Functions
KEY: Conceptual Understanding
62. ANS:
PTS: 1
DIF: Moderate
REF: 6.5 Slope-Point Form of the Equation for a Linear Function
LOC: 10.RF7
TOP: Relations and Functions
KEY: Conceptual Understanding
63. ANS:
or
PTS:
REF:
LOC:
KEY:
64. ANS:
1
DIF: Moderate
6.5 Slope-Point Form of the Equation for a Linear Function
10.RF7
TOP: Relations and Functions
Conceptual Understanding | Procedural Knowledge
PTS: 1
LOC: 10.RF6
65. ANS:
DIF: Easy
REF: 6.6 General Form of the Equation for a Linear Relation
TOP: Relations and Functions
KEY: Conceptual Understanding
PTS: 1
LOC: 10.RF6
66. ANS:
DIF: Easy
REF: 6.6 General Form of the Equation for a Linear Relation
TOP: Relations and Functions
KEY: Conceptual Understanding
PTS: 1
LOC: 10.RF6
DIF: Easy
REF: 6.6 General Form of the Equation for a Linear Relation
TOP: Relations and Functions
KEY: Conceptual Understanding
PROBLEM
67. ANS:
Sketch a diagram.
rise
25 m
The guy wire is attached to the building 40 m above the ground.
PTS: 1
DIF: Moderate
REF: 6.1 Slope of a Line
LOC: 10.RF5
TOP: Relations and Functions
KEY: Problem-Solving Skills
68. ANS:
a) Point A has coordinates (–3, 4).
Point B has coordinates (1, –4).
From A to B:
The rise is the change in y-coordinates.
Rise =
= –8
The run is the change in x-coordinates.
Run =
=4
b) Sample answer:
6
Q
y
R
J
4
A
2
–6
–4
–2
0
2
4
6 x
–2
–4
K
B
–6
Any horizontal line segment has slope 0. The slope of QR is zero.
Any vertical line segment has a slope that is not defined. The slope of JK is not defined.
The slope of AB is the same as the slope of the line segment in part a. It has a rise of –8 and a run of 4.
PTS: 1
DIF: Moderate
REF: 6.1 Slope of a Line
LOC: 10.RF5
TOP: Relations and Functions
KEY: Problem-Solving Skills
69. ANS:
a) Determine the slope of RK.
Slope of RK =
Slope of RK =
Slope of RK =
Slope of RK =
The slope of line RK is
.
b) The slope of a line parallel to RK has the same slope as RK, which is
.
The slope of VB is
.
c) The slope of a line perpendicular to RK is the negative reciprocal of
, which is 2.
The slope of WX is 2.
PTS: 1
DIF: Moderate
REF: 6.2 Slopes of Parallel and Perpendicular Lines
LOC: 10.RF3
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
70. ANS:
The graph has a slope of
6
and a y-intercept of 2.
y
4
2
–6
–4
–2
0
2
4
6 x
–2
–4
–6
PTS: 1
DIF: Moderate
REF: 6.3 Investigating Graphs of Linear Functions
LOC: 10.RF7
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
71. ANS:
a) The student may have interchanged the signs of the slope and y-intercept.
b) Use the equation:
To write the equation of a linear function, determine the slope of the line, m, and its y-intercept, b.
The line intersects the y-axis at 2; so,
.
From the graph, the rise is
when the run is .
So,
, or
Substitute for m and b in
The equation of the graph is:
PTS: 1
DIF: Moderate
.
REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function
LOC: 10.RF6
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
72. ANS:
Use the equation:
To write the equation of a linear function, determine the slope of the line, m, and its y-intercept, b.
The line intersects the y-axis at ; so,
.
From the graph, the rise is 4 when the run is 5.
So,
Substitute for m and b in
.
An equation for the function is:
To verify the equation, substitute the coordinates of a point on the line into the equation. Choose the point (0,
).
Substitute
and
into the equation:
Since the left side is equal to the right side, the equation is correct.
PTS: 1
DIF: Moderate
REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function
LOC: 10.RF6
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills
73. ANS:
Graph A: slope 4; y-intercept 0
Graph B: slope
; y-intercept 0
Graph C: slope
; y-intercept
Graph D: slope
; y-intercept 0
PTS: 1
DIF: Moderate
REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function
LOC: 10.RF6
TOP: Relations and Functions
KEY: Problem-Solving Skills
74. ANS:
a)
Identify the coordinates of one point on
the line and calculate the slope.
y
4
The coordinates of one point are (–2, –3).
To calculate the slope, m, use:
2
–4
–2
0
2
4
x
–2
(–2, –3)
–4
Use the slope-point form of the equation.
Substitute
,
, and
.
In slope-point form, the equation of the line is:
b)
In slope-intercept form, the equation of the line is:
From the equation, the y-intercept is –2.
PTS: 1
DIF: Moderate
REF: 6.5 Slope-Point Form of the Equation for a Linear Function
LOC: 10.RF7
TOP: Relations and Functions
KEY: Problem-Solving Skills
75. ANS:
Rewrite the equation in slope-intercept form.
From the equation, the slope of the line is
the negative reciprocal of
. Any line perpendicular to
; that is, its slope is
has a slope that is
.
PTS: 1
DIF: Moderate
REF: 6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF7 | 10.RF5
TOP: Relations and Functions
KEY: Problem-Solving Skills
76. ANS:
Since the coordinates of 2 points on the line are known, use this form for the equation of a linear function:
Substitute:
,
,
, and
In general form, an equation that represents the line that passes through A(3, –4) and B(11, 8) is:
PTS: 1
DIF: Moderate
LOC: 10.RF7 | 10.RF5
KEY: Problem-Solving Skills
REF: 6.6 General Form of the Equation for a Linear Relation
TOP: Relations and Functions
77. ANS:
a)
so two points on the graph have coordinates A(27, 500) and B(90, 605).
Use this form for the equation of a linear function:
Substitute:
,
,
, and
In general form, the equation that represents this function is:
b) Use:
Substitute:
When the temperature of the air is 60°C, its volume is 555 mL.
c) Use:
Substitute:
When the volume of the air is 1010 mL, its temperature is 333°C.
PTS: 1
DIF: Difficult
LOC: 10.RF7 | 10.RF5
KEY: Problem-Solving Skills
78. ANS:
Sample answer:
Determine the x- and y-intercepts.
REF: 6.6 General Form of the Equation for a Linear Relation
TOP: Relations and Functions
To determine the x-intercept, substitute y = 0:
The x-intercept is 4 and is described by the point (4, 0).
To determine the y-intercept, substitute x = 0:
The y-intercept is
and is described by the point (0,
On a grid, plot the points that represent the intercepts.
Draw a line through the points.
).
y
8
4
–16
–12
–8
–4
0
–4
4
8
12
16
x
x - 4y - 4 = 0
–8
PTS: 1
DIF: Moderate
REF: 6.6 General Form of the Equation for a Linear Relation
LOC: 10.RF7 | 10.RF5
TOP: Relations and Functions
KEY: Communication | Problem-Solving Skills