Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
Graph the linear equation in two variables.
1)
1)
y = – 3x – 3
A)
B)
C)
D)
Use the given conditions to write an equation for the line in slope–intercept form.
2)
2)
Passing through (5, 5) and parallel to the line whose equation is y = – 6x.
A)
y = – 6x + 35
B)
y = – 6x – 35
C)
y = – 1
6x –35
6
D)
y =6x – 35
Graph the equation.
3)
3)
6x = – 30
A)
B)
C)
D)
2
Put the equation in slope–intercept form by solving for y. Use the slope and y–intercept to graph the equation.
4)
4)
6x + y =5
A)
B)
C)
D)
Find the x–intercept and the y–intercept of the graph of the equation. Do not graph the equation.
5)
5)
4x – 20y =20
A)
x–intercept = – 1; y–intercept =5
B)
x–intercept =5; y–intercept = – 1
C)
x–intercept =5; y–intercept =1
D)
x–intercept =1; y–intercept =5
Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate
whether the line rises, falls, is horizontal, or is vertical.
6)
6)
(–5, 9) and (–5, 5)
A)
m = 1; rises
B)
undefined slope; vertical
C)
m = 0; horizontal
D)
m = – 1; falls
Use the given conditions to write an equation for the line in point–slope form and slope–intercept form.
7)
7)
Passing through (4, –18) and (1, –6)
A)
y + 18 = – 4(x – 4) or y + 6 = – 4(x – 1); y = – 4x + 2
B)
y + 18 =4(x – 4) or y + 6 =4(x – 1); y =4x – 2
C)
y + 18 = – 4(x – 4) or y + 6 = – 4(x – 1); y = – 4x – 2
D)
y + 18 =4(x – 4) or y + 6 =4(x – 1); y =4x + 2
Plot the given point in a rectangular coordinate system.
8)
8)
(–4, 0)
4
A)
B)
C)
D)
Find the y– and x–intercepts for the equation. Then graph the equation.
9)
9)
2y – x = 0
5
A)
(0, 0), (0, 0)
B)
(0, –2), (2, 0)
C)
(0, 2), (–2, 0)
D)
(0, 0), (0, 0)
Find the slope of the line.
10)
10)
y =4x
A)
0
B)
1
4
C)
4
D)
–4
Determine whether the lines through each pair of points are perpendicular.
11)
11)
(8, –3) and (0, 7); (–7, 6) and (–2, 2)
A)
not perpendicular
B)
perpendicular
Plot the given point in a rectangular coordinate system.
12)
–3
2, 0
12)
A)
B)
C)
D)
Find the point–slope form of the equation of the line satisfying the given conditions and use this to write the
slope–intercept form of the equation.
13)
x–intercept =5
2 and y–intercept =5
13)
A)
y = – 2x + 5
B)
y = – 2
5x + 5
C)
y = – 2x + 10
D)
y = – 2x – 5
Use the given conditions to write an equation for the line in slope–intercept form.
14)
14)
Passing through (5, –5) and parallel to the line whose equation is 2x + y =3.
A)
y =2x – 5
B)
y = – 2x + 5
C)
y = – 2x – 5
D)
y = – 1
2x –5
2
Find the slope and the y–intercept of the line with the given equation.
15)
15)
y =2x + 8
A)
m =1
2; y–intercept =8
B)
m =2; y–intercept =8
C)
m = – 2; y–intercept = – 8
D)
m =8; y–intercept =2
Find the point–slope form of the equation of the line satisfying the given conditions and use this to write the
slope–intercept form of the equation.
16)
16)
Slope =5, passing through (2, 4)
A)
y =5x – 6
B)
y = – 5x + 6
C)
y =1
5x –6
5
D)
y =5x + 6
Solve the problem.
17)
17)
The linear equation in two variables y =3x +80 models the total cost, y, in dollars, for towing a
car x miles. The equation indicates that the towing company charges a fixed amount of $80 to
send a truck to pick up the car plus a cost of $3 for each mile the car is towed. Find a solution of
y =3x +80 using 13 for x.
A)
(13, 119)
B)
(13, 83)
C)
(13, 109)
D)
(13, 39)
Find the slope of the line passing through the pair of points or state that the slope is undefined.
18)
18)
(–12, –13) and (–3, –2)
A)
11
9
B)
–11
9
C)
9
11
D)
1
Solve the problem.
19)
19)
A customer at a store bought 8 bottles of juice and 4 fruit pies for a total cost of $60.00. If a bottle
of juice costs $3.25, find the cost of a fruit pie.
A)
$7.50
B)
$9.25
C)
$8.50
D)
$8.00
Find the y–intercept.
20)
20)
y = – 9
A)
–9
B)
1
9
C)
1
D)
0
Plot the given point in a rectangular coordinate system.
9
21)
21)
(–4, 3)
A)
B)
C)
D)
Find the slope of the line and write the slope as a rate of change. Don’t forget to attach the proper units.
22)
22)
The graph shows the total cost y (in dollars) of owning and operating a mini–van where x is the
number of miles driven.
A)
cannot be determined
B)
$2.20 per mile
C)
$32.00 per mile
D)
$0.45 per mile
Determine whether the lines through each pair of points are parallel, perpendicular, or neither.
23)
23)
(–8, –4) and (–16, –22); (2, 7) and (6, –2)
A)
neither
B)
parallel
C)
perpendicular
Find the slope.
24)
Find the slope of a line parallel to the line y = – 3
4x.
24)
A)
0
B)
4
3
C)
–3
4
D)
undefined
Find three solutions to the given equation using the table of values. Then use the three solutions in the table to graph
the equation.
11
25)
25)
y =3x – 5
x y
–1
0
1
A)
(–1, 5), (0, 0), (1, –5)
B)
(–1, –2), (0, –5), (1, –8)
C)
(–1, 2), (0, 5), (1, 8)
D)
(–1, –8), (0, –5), (1, –2)
Find an equation for the line with the given properties.
26)
26)
The solid line L contains the point (2, 5) and is parallel to the dotted line whose equation is y =2x.
Give the equation for the line L in slope–intercept form.
A)
y =2x + 1
B)
y – 5 =2(x –2)
C)
y = 2x + b
D)
y =2x + 3
Find the x–intercept and the y–intercept of the graph of the equation. Do not graph the equation.
27)
27)
3x + y =3
A)
x–intercept = – 2; y–intercept =9
B)
x–intercept =3; y–intercept =1
C)
x–intercept =1; y–intercept =3
D)
x–intercept =1; y–intercept = 0
13
The graph shows the monthly revenue in millions of dollars of a growing company after the company doubled its
advertising. Use the graph to solve the problem.
28)
28)
During what period of time is the company‘s monthly revenue decreasing?
A)
From the time that the advertising was doubled until the 6th month
B)
From the 9th month to the 12th month
C)
From the 6th month to the 9th month
D)
From the time that the advertising was doubled until the 9th month
Graph the linear equation using the slope and y–intercept.
29)
y =3
4x + 5
29)
14
A)
B)
C)
D)
Find the point–slope form of the equation of the line satisfying the given conditions and use this to write the
slope–intercept form of the equation.
30)
Slope =6
7, passing through (0, 6)
30)
A)
y = – 6
7x – 6
B)
y =6
7x + 6
C)
y =6
7x – 6
D)
y =7
6x + 7
Use the given conditions to write an equation for the line in slope–intercept form.
31)
Passing through (2, 3) and parallel to the line whose equation is y = – 1
9x +4.
31)
A)
y = – 9x – 29
B)
y =1
9x –29
9
C)
y = – 1
9x +29
9
D)
y = – 1
9x –29
9
Plot the given point in a rectangular coordinate system.
32)
32)
(6, –3)
A)
B)
C)
D)
Graph the linear equation using the slope and y–intercept.
33)
33)
y =5x + 5
A)
B)
C)
D)
Find the slope.
34)
34)
Find the slope of a line parallel to the line y =5.
A)
1
5
B)
0
C)
5
D)
undefined
Graph the equation.
35)
35)
x =6
A)
B)
C)
D)
Find the x–intercept and the y–intercept of the graph of the equation. Do not graph the equation.
36)
36)
10x – 2y = – 6
A)
x–intercept = – 3
5; y–intercept = – 3
B)
x–intercept =3
5; y–intercept =3
C)
x–intercept =3; y–intercept = – 3
5
D)
x–intercept = – 3
5; y–intercept =3
Find the slope of the line passing through the pair of points or state that the slope is undefined.
37)
37)
(–8, 7) and (3, 4)
A)
–11
5
B)
–11
3
C)
3
11
D)
–3
11
Determine whether the lines through each pair of points are perpendicular.
38)
38)
(3, 10) and (–9, 14); (–2, 8) and (0, 14)
A)
perpendicular
B)
not perpendicular
Find the point–slope form of the equation of the line satisfying the given conditions and use this to write the
slope–intercept form of the equation.
39)
39)
x–intercept = – 6 and y–intercept =1
A)
y = – 1
6x + 1
B)
y =1
6x + 2
C)
y =6x + 1
D)
y =1
6x + 1
Find the x–intercept and the y–intercept of the graph of the equation. Do not graph the equation.
40)
40)
–2x + 2y =10
A)
x–intercept =5; y–intercept = – 5
B)
x–intercept = – 2; y–intercept = 0
C)
x–intercept = – 2; y–intercept =6
D)
x–intercept = – 5; y–intercept =5
Write an equation in slope–intercept form of the line satisfying the given conditions.
41)
41)
Perpendicular to the line x + 4y = – 4; containing the point (–3, 3).
A)
y =4x + 15
B)
y =4x + 9
C)
y = – 1
4x +15
4
D)
y =1
4x +15
4
Provide an appropriate answer.
42)
42)
Determine whether the points whose coordinates are (–2, 3), (–1, 4), and (0, 5) lie on a line.
A)
The points do not lie on a line.
B)
The points lie on a line.