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Linear Equations Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. The y-intercept of the line y = –4x – 7 is
a. 7
b. 4
2
2. What is the y-intercept of the line y =  x?
3
2
a. 
3
b.
____
0
2
3. What is the slope of the line y =  x ?
3
2
a. 
3
b.
0
c.
d.
4
7
c.
1
d.
3
2
c.
d.
2
3
3
2
____
4. Identify the equation of the line with a slope of –3 and a y-intercept of 4.
a. y = 3x + 4
c. y = –3x + 4
b. y = 3x – 4
d. y = –3x – 4
____
5. Rewrite the equation y = –2x + 5 in general form.
a. –2x + y – 5 = 0
c.
b. –2x – y + 5 = 0
d.
____
____
2x – y + 5 = 0
2x + y – 5 = 0
2
?
3
2
–5x – y – = 0
3
6. Which of the following is equivalent to the equation y = –5x –
a.
15x + 3y + 2 = 0
b.
5x + y +
2
=0
3
c.
d.
–15x – 3y – 2 = 0
7. What is the equation y = 0.25x – 0.75 in general form?
a. –x + 4y – 3 = 0
c. x – 4y – 3 = 0
b. –x + 4y + 3 = 0
d. x – 4y + 3 = 0
____
8. What are the slope and y-intercept of this line?
a.
b.
____
slope: –2, y-intercept: –1
slope: –2, y-intercept: 1
c.
d.
slope: 2, y-intercept: –1
slope: 2, y-intercept: 1
9. What is the slope of the line passing through points (x, y) and (p, q)?
px
q p
a.
c.
q y
y x
q y
x y
b.
d.
px
q p
____ 10. Which equation represents the line containing points M and N?
1
x–3
4
a.
y = –4x – 3
c.
y=
b.
1
y= x–3
4
d.
y = 4x – 3
____ 11. For the line 3x – 4y – 12 = 0, which statement is true?
a. The x-intercept is 3 and the y-intercept is 4.
b. The x-intercept is 3 and the y-intercept is –4.
c. The x-intercept is 4 and the y-intercept is 3.
d. The x-intercept is 4 and the y-intercept is –3.
____ 12. When a linear equation is written in the form Ax + By + C = 0, A and B cannot both be
a. fractions
c. one
b. integers
d. zero
____ 13. Rewrite the equation 4x + y + 2 = 0 in slope-intercept form.
a. y = 4x + 2
c. y = –4x + 2
b. y = 4x – 2
d. y = –4x – 2
____ 14. What is the equation 8x – 4y – 12 = 0 in slope-intercept form?
a. y = –2x – 3
c. y = 2x – 3
b. y = –2x + 3 `
d. y = 2x + 3
____ 15. The equation 3x – 6y – 2 = 0 in slope-intercept form is
1
1
a. y =  x –
c. y =
2
3
1
1
b. y =  x +
d. y =
2
3
1
x–
2
1
x+
2
1
3
1
3
____ 16. What are the slope and y-intercept of the relation represented by the equation 10x + 5y – 15 = 0?
a. slope: 2, y-intercept: 3
c. slope: –2, y-intercept: 3
b. slope: 2, y-intercept: –3
d. slope: –2, y-intercept: –3
____ 17. The slope and y-intercept of the relation represented by the equation 12x – 9y + 2 = 0 are
4
2
4
2
a. slope:  , y-intercept: 
c. slope: , y-intercept: 
3
9
3
9
4
2
4
2
b. slope:  , y-intercept:
d. slope: , y-intercept:
3
9
3
9
____ 18. For the line 4x – 3y – 12 = 0, which statement is true?
a. The x-intercept is 3 and the y-intercept is –4.
b. The x-intercept is 3 and the y-intercept is 4.
c. The x-intercept is 4 and the y-intercept is –3.
d. The x-intercept is 4 and the y-intercept is 3.
____ 19. What is the slope of the line with an x-intercept of 4 and a y-intercept of –3?
4
3
a. 
c.
3
4
3
4
b. 
d.
4
3
____ 20. Identify the equation in general form for the line with slope 3 and y-intercept –4.
a. 3x – y – 4 = 0
c. 3x + y – 4 = 0
b. 3x – y + 4 = 0
d. 3x + y + 4 = 0
____ 21. Identify the equation of the line in general form when the slope is 0.6 and the y-intercept is 0.4.
a. 3x + 5y + 2 = 0
c. 3x – 5y + 2 = 0
b. 3x + 5y – 2 = 0
d. 3x – 5y – 2 = 0
____ 22. Points C(5, 7) and D(–3, –12) are on a line. What is the run from point D to point C?
a. 8
c. 8
b. 5
d. 
____ 23. Points M(2, 9) and N(–1, 3) are on a line with y-intercept –4. What is the equation of the line?
a. y = –4x – 2
c. y = 2x – 4
b. y = –2x + 4
d. y = 4x + 2
____ 24. Identify the slope of the line through points (3, 4) and (–4, –5).
9
a. 
c. 0
7
9
b. –1
d.
7
____ 25. The equation of the line through the point (2, 3) with slope –2 is
a. y = –2x + 7
c. y = –2x + 1
b. y = –2x + 3
d. y = –2x – 1
____ 26. Using the table of values, determine the equation of the line.
a.
b.
y = –3x – 9
y = –3x + 3
____ 27. The equation of the line with slope
a.
b.
1
x+9
3
1
y= x+3
3
y=
____ 28. Which two lines are parallel?
a. y = 3x + 2
y = 2x + 2
b. y = 3x – 4
y=x+5
c.
d.
y = 3x – 9
y = 3x + 3
1
that passes through the point (0, –3) is
3
1
c. y = x – 9
3
1
d. y = x – 3
3
c.
d.
y=x
y=5
y=0
y=2
____ 29. Identify the pair of perpendicular lines.
1
a. y = x + 2
5
1
y= x+1
5
1
b. y = x + 2
5
y = 5x + 1
c.
d.
2
x+1
3
2
y= x+2
3
2
y= x+1
3
3
y=– x+2
2
y=
____ 30. What is the equation of the line that passes through (3, –1) and is parallel to the line y = 3x + 2?
x
a. y = 3x + 10
c. y = + 8
3
x
b. y = 3x – 10
d. y = – 10
3
____ 31. What is the equation of the line that is perpendicular to the line y = –3x + 2 and passes through (3, –1)?
1
1
a. y = x
c. y = – x
3
3
1
1
b. y = x – 2
d. y = – x – 2
3
3
____ 32. Identify the equation of the line parallel to y = 2x – 4 and with the same x-intercept as 3x – 4y = 12.
1
a. y = 2x + 4
c. y =  x + 8
2
1
b. y = 2x – 8
d. y =  x + 4
2
____ 33. The equation of line A is y = 4x – 8. Which equation represents a line that is parallel to line A?
a. y = 8x – 4
c. y = –4x – 8
b. y = 4x + 8
d. y = –8x + 4
____ 34. The equation of line A is y = 2x.
The equation of line B is y = –2x.
The equation of line C is y = 2x + 2.
The equation of line D is y = 2x – 2.
Which lines are parallel to line A?
a. line B only
b. line B and line D
c.
d.
line C and line D
line B, line C, and line D
____ 35. The equation of line T is y = 5x + 10, while the equation of line U is y = 4x + 10. Which statement is true?
a. Line T is parallel to line U.
c. Line T is steeper than line U.
b. Line U is perpendicular to line T.
d. Line U is steeper than line T.
____ 36. Points G(–3, 8) and H(0, 5) are on a line. Which equation represents a line that is parallel to this line?
a. y = 2x – 8
c. y = –x + 5
b. y = x – 5
d. y = –2x + 8
____ 37. Which equation represents a line that is perpendicular to a line passing through points G(–3, 8) and H(0, 5)?
a. y = –2x + 5
c. y = x – 5
b. y = –x + 8
d. y = 2x – 8
Completion
Complete each statement.
1. In the equation of a line, y = 4x – 3, the number –3 represents the _________________________ .
2. Points M(2, –8) and N(0, –4) are on a line. The slope of the line is _________________________ and the
y-intercept is _________________________ . The equation of the line is _________________________ .
3. The x-intercept occurs when _________________________ .
3
4. The slope of the line represented by y – 2 =  (x + 5) is _________________________ .
4
5. Two lines that have the same slope are said to be _________________________ .
6. Perpendicular lines have slopes that are _________________________ .
Matching
Match each statement to the corresponding term. Each term may be used more than once or not at all.
a.
b.
c.
d.
e.
f.
general form
negative reciprocals
parallel lines
perpendicular lines
point of intersection
reciprocals
g.
h.
i.
j.
k.
slope
slope-intercept form
slope-point form
x-intercept
y-intercept
____
1. For a horizontal line, this is zero.
____
2. These lines have the same slope.
____
3. For a vertical line, the value of x is constant and equal to this.
____
4. This is where two lines meet.
____
5. For the line y = 3x + 6, this is 6.
____
6. The numbers 3 and
____
7. These lines meet at 90°.
____
8. This is the name for an equation of a line in the form Ax + By + C = 0.
____
9. This is the form usually used to show the equation of a line if you know the coordinates of the y-intercept and
the slope.
____ 10. The numbers
1
are examples.
3
2
3
and  are examples.
3
2
Linear Equations Review
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
A
B
A
C
D
A
C
C
B
B
D
D
D
C
C
C
D
Rewrite the equation 12x – 9y + 2 = 0 in slope-intercept form:
12x – 9y + 2 = 0
12x – 9y + 2 + 9y = 0 + 9y
12x + 2 = 9y
12x 2 9y
+ =
9
9 9
4
2
x+ =y
3
9
4
2
y= x+
3
9
4
2
The slope is and the y-intercept is .
3
9
A
C
A
C
C
C
D
A
26. C
Choose any two points to calculate the slope. For example, use (0, –9) and (1, –6):
rise
m
run
27.
28.
29.
30.
31.
m
6  (9)
10
m
3
1
m3
From the table, the y-intercept is –9.
Substitute m = 3 and b = –9 into y = mx + b:
y = mx + b
= 3x – 9
The equation of the line is y = 3x – 9.
D
D
D
B
The line must also have slope 3. Substitute the slope and the coordinates of the point (3, –1) into the equation y
= mx + b and solve for b:
y = mx + b
–1 = (3)(3) + b
–1 = 9 + b
–1 – 9 = 9 + b – 9
–10 = b
The equation of the line is y = 3x – 10.
B
1
The slope of the line must be the negative reciprocal of –3, or :
3
y = mx + b
 1 
–1 =   (3) + b
3
–1 = 1 + b
–1 – 1 = 1 + b – 1
–2 = b
The equation of the line is y =
1
x – 2.
3
32. B
The line must have slope 2. Identify the x-intercept of 3x – 4y = 12.
Substitute y = 0:
3x – 4y = 12
3x – 4(0) = 12
3x = 12
3x 12
=
3
3
x=4
The point (4, 0) is on the line. Substitute the slope and this point into y = mx + b:
y = mx + b
0 = (2)(4) + b
0=8+b
0–8=8+b–8
–8 = b
The equation of the line is y = 2x – 8.
33. B
The line represented by the equation y = 4x + 8 is parallel to line A because they both have slope 4.
34. C
Line A has slope 2. Lines C and D have slope 2, which is the same as that of line A. Line B has slope –2. So,
Lines C and D are parallel to line A.
35. C
Line T has a slope of 5, while line U has a slope of 4. Because line T has a greater slope, it is steeper than line
U.
36. C
rise
m
run
m
58
0  (3)
m
3
3
m  1
Parallel lines have the same slope. The only line that has a slope of –1 is y = –x + 5.
37. C
rise
m
run
m
58
0  (3)
m
3
3
m  1
Perpendicular lines have slopes that are negative reciprocals. The only line that has a slope of +1 is y = x – 5.
COMPLETION
1. y-intercept
2. –2; –4; y = –2x – 4
3. y = 0
3
4. 
4
5. parallel
6. negative reciprocals
MATCHING
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
G
C
J
E
K
F
D
A
H
B