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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.

0

A

B

2 4–2–4 x

2

4

–2

–4

y

a. 2

3

c. 2

3

b. 3

2

d. 3

2

____ 2. Which line segment has slope 7

4?

i)

0

A

B

2 4–2–4 x

2

4

–2

–4

y

ii)

0

A

B

2 4–2–4 x

2

4

–2

–4

y

iii) iv)

0

AB

2 4–2–4 x

2

4

–2

–4

y

0

A

B

2 4–2–4 x

2

4

–2

–4

y

a. iii c. i

b. ii d. iv

____ 3. Determine the slope of the line that passes through G(3, –3) and H(–5, 9).

a. 3

2

c. 2

3

b. 2

3

d. 3

2

____ 4. Is the slope of this line segment positive, negative, zero, or not defined?

0

S

T

4 8–4–8 x

4

8

–4

–8

y

a. zero c. not defined

b. positive d. negative


0

R S

4 8–4–8 x

4

8

–4

–8

y

a. positive c. zero

b. negative d. not defined


0

B

C4 8–4–8 x

4

8

–4

–8

y

a. negative c. positive

b. not defined d. zero


0

V

W

4 8–4–8 x

4

8

–4

–8

y

a. positive c. not defined

b. negative d. zero

____ 8. Determine the steepness of this roof by calculating its slope.

rise

run

a. 5

3

c. 3

5

b. 5

3

d. 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.

d.

____ 10. Which of these line segments are parallel?

0A

B

E

F

C

D

G

H

2 4–2–4 x

2

4

–2

–4

y

a. CD and EF c. AB and CD

b. EF and GH d. AB and EF

____ 11. Determine the slope of the line that is perpendicular to this line segment.

0

A

B

2 4–2–4 x

2

4

–2

–4

y

a. 3 c. 1

3

b. –3 d. –

1

3

____ 12. Determine the slope of the line that is parallel to this line segment.

0

K

X

2 4–2–4 x

2

4

–2

–4

y

a.

–3

7

c. 3

7

b. 7

3

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. 15

17

c. –15

b. 17

15

d. 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

3

c. 2

3

b. 3

2

d. 3

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.

–1

5

d. 1

5

____ 16. A line has x-intercept 4 and y-intercept –5. Determine the slope of a line perpendicular to this line.

a. 4

5

c. 5

4

b. 5

4

d. 4

5

____ 17. The slope of this line is . What is the equation of the line?

0 2 4–2–4 x

2

4

–2

–4

y

a.

y = c.

y =

b. y = d. 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

x-intercept.

d. None of the above.

____ 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.

c. All the graphs will have the same slope.

b. All the graphs will have the same

x-intercept.

d. None of the above.

____ 20. The slope of this line is . What is the equation of the line?

0 2 4–2–4 x

2

4

6

8

–2

–4

–6

–8

y

a.

c.

b.

d.

____ 21. Write an equation for the graph of a linear function that has slope and y-intercept –3.

a.

c.

b.

d.

____ 22. Which graph represents the equation ?

a. c.

0 2 4–2–4 x

2

4

–2

–4

y

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

y

d.

0 2 4–2–4 x

2

4

–2

–4

y

____ 23. Write an equation to describe this graph.

0 2 4–2–4 x

2

4

–2

–4

y

a.

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.

0 2 4–2–4 x

2

4

–2

–4

y

c.

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

y

d.

0 2 4–2–4 x

2

4

–2

–4

y


0 10 20–10–20 t

10

20

–10

–20

d

a. c. b. d.


0 6 12–6–12 x

6

12

–6

–12

y

a.

c.

b.

d.

____ 29. Write an equation for the graph of a linear function that has slope 1 and y-intercept 8.

a. c.

b. 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. slope: 9; y-intercept:

d. slope: ; y-intercept: 3

____ 31. Determine the slope and y-intercept of this graph.

0 2 4–2–4 x

2

4

–2

–4

y

a. slope: ; y-intercept: –1.5

c. slope: ; y-intercept: 1.5

b. slope: ; y-intercept: 1.5

d. slope: ; y-intercept: –1.5

____ 32. Which equations represent parallel lines?

a. , c. ,

b. , d. ,

____ 33. Which equations represent perpendicular lines?

a. , c. ,

b. ,

d. ,

____ 34. Describe the graph of the linear function with this equation:

a. The graph is a line through (–2, 3) with slope .

b. The graph is a line through (2, ) with slope .

c. The graph is a line through (2, ) with slope .

d. 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.


a.

0 2 4–2–4 x

2

4

–2

–4

y

c.

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

y

d.

0 2 4–2–4 x

2

4

–2

–4

y

____ 38. Write an equation in slope-point form for this line.

0 2 4–2–4 x

2

4

–2

–4

y

a.

c.

b.

d.

____ 39. Write this equation in slope-intercept form:

a.

13

5

c.

13

5

b.

13

5

d.

13

5


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 written?

a. Standard form c. General form

b. Slope-intercept form d. Slope-point form

____ 48. Write this equation in general form:

a. c.

b. d.


a. c.

b. d.


a. c.

b. 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. c.

b. d.


a. c.

0 2 4–2–4 x

2

4

–2

–4

y

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

y

d.

0 2 4–2–4 x

2

4

–2

–4

y

____ 54. Determine the slope of the line with this equation:

a. –

7

3

c. 7

3

b. 3

7

d. –

3

7

____ 55. Determine the slope of the line with this equation:

a. –4 c.

b.

d. 4


a. y =

10

3x +

4

3

c. y =

10

3x –

4

3

b. y = –

10

3x +

4

3

d. y = –

10

3x – 4


a. c.

0 2 4–2–4 x

2

4

–2

–4

y

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

y

d.

0 2 4–2–4 x

2

4

–2

–4

y

____ 58. Which equation is equivalent to ?

a.

c.

b.

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

the ramp must be 3

32. The entrance to the school is 75 cm above the ground. What is the horizontal distance

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

slope of 8

5. How high up the tower does the wire reach?

68. a) Determine the rise, run, and slope of this line segment.

0

A

B

2 4–2–4 x

2

4

–2

–4

y

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?

0 2 4–2–4 x

2

4

–2

–4

y

72. Write an equation to describe this function. Verify the equation.

0 2 4–2–4 x

2

4

–2

–4

y

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 ; y-intercept 0

Graph A

Graph B

0 2 4–2–4 x

2

4

–2

–4

y

0 2 4–2–4 x

2

4

–2

–4

y

Graph C

0 2 4–2–4 x

2

4

–2

–4

y

Graph D

0 2 4–2–4 x

2

4

–2

–4

y

74. a) Write an equation in slope-point form for this line.

0 2 4–2–4 x

2

4

–2

–4

y

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.

0 4 8 12 16–4–8–12–16 x

4

8

–4

–8

y

unit 6 review for final

Answer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 DIF: Easy REF: 6.1 Slope of a Line

LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

2. ANS: C PTS: 1 DIF: Easy REF: 6.1 Slope of a Line


3. ANS: D PTS: 1 DIF: Easy REF: 6.1 Slope of a Line



LOC: 10.RF5 TOP: Relations and Functions KEY: Conceptual Understanding



6. ANS: A PTS: 1 DIF: Easy REF: 6.1 Slope of a Line


7. ANS: A PTS: 1 DIF: Easy REF: 6.1 Slope of a Line


8. ANS: B PTS: 1 DIF: Easy REF: 6.1 Slope of a Line


9. ANS: B PTS: 1 DIF: Moderate REF: 6.1 Slope of a Line


10. ANS: D PTS: 1 DIF: Easy

REF: 6.2 Slopes of Parallel and Perpendicular Lines LOC: 10.RF3

TOP: Relations and Functions KEY: Procedural Knowledge




12. ANS: C PTS: 1 DIF: Easy












16. ANS: A PTS: 1 DIF: Easy




REF: 6.3 Investigating Graphs of Linear Functions LOC: 10.RF7

TOP: Relations and Functions KEY: Conceptual Understanding










21. ANS: B PTS: 1 DIF: Easy

REF: 6.4 Slope-Intercept Form of the Equation for a Linear Function
































32. ANS: D PTS: 1 DIF: Moderate



33. ANS: B PTS: 1 DIF: Moderate




REF: 6.5 Slope-Point Form of the Equation for a Linear Function










LOC: 10.RF6 TOP: Relations and Functions

KEY: Conceptual Understanding | Procedural Knowledge




39. ANS: A PTS: 1 DIF: Moderate



40. ANS: B PTS: 1 DIF: Moderate



















45. ANS: D PTS: 1 DIF: Moderate




46. ANS: C PTS: 1 DIF: Moderate





REF: 6.6 General Form of the Equation for a Linear Relation LOC: 10.RF6













TOP: Relations and Functions KEY: Conceptual Understanding | Procedural Knowledge



















58. ANS: C PTS: 1 DIF: Moderate



SHORT ANSWER

59. ANS:

800 cm, or 8 m

PTS: 1 DIF: Moderate REF: 6.1 Slope of a Line


60. ANS:

0 2 4–2–4 x

2

4

–2

–4

y

PTS: 1 DIF: Easy



61. ANS:

PTS: 1 DIF: Easy



62. ANS:

PTS: 1 DIF: Moderate



63. ANS:

or





64. ANS:

PTS: 1 DIF: Easy REF: 6.6 General Form of the Equation for a Linear Relation


65. ANS:



66. ANS:



PROBLEM

67. ANS:

Sketch a diagram.

rise

25 m

The guy wire is attached to the building 40 m above the ground.


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:

0

A

B

J

K

Q R

2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

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.



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


KEY: Communication | Problem-Solving Skills

70. ANS:

The graph has a slope of and a y-intercept of 2.

0 2 4 6–2–4–6 x

2

4

6

–2

–4

–6

y

PTS: 1 DIF: Moderate REF: 6.3 Investigating Graphs of Linear Functions



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:





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.





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




74. ANS:

a)

Identify the coordinates of one point on

the line and calculate the slope.

The coordinates of one point are (–2, –3).

To calculate the slope, m, use:

0

(–2, –3)

2 4–2–4 x

2

4

–2

–4

y

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.




75. ANS:

Rewrite the equation in slope-intercept form.

From the equation, the slope of the line is . Any line perpendicular to has a slope that is

the negative reciprocal of ; that is, its slope 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:




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 REF: 6.6 General Form of the Equation for a Linear Relation



78. ANS:

Sample answer:

Determine the x- and y-intercepts.

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.

0

x - 4y - 4 = 0

4 8 12 16–4–8–12–16 x

4

8

–4

–8

y




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