Parallel, Perpendicular or Neither
Name ________________

To decide if lines are parallel or perpendicular, first write the lines in
___________________________ form, which is ___________________.

Parallel lines have slopes that are ____________________________.

Perpendicular lines have slopes that are ________________________________.
State whether the lines are parallel, perpendicular, or neither.
y = 6x - 3
y = 3x + 2
1.
2.
1
2y = 6 x - 6
y =- x+7
6
3x + 2 y = 5
4.
3y + 2x = - 3
7.
y = x+3
y =-x- 5
y - 5 = 6x
5.
y - 6x = - 1
8.
y = 6
x =- 2
3.
8 x - 2y = 3
x + 4y = - 1
y = 3x + 9
6.
9.
y =
1
x- 4
3
3y = - x
3x = y
10. Decide if the lines are perpendicular: y 
1
x  10 and y  3x .
3
5
x  2?
7
7
C) y   x  3
5
11. Which of the following lines is parallel to y  
A) y 
5
x  5
7
B) y 
12. A line parallel to y 
2
A) y   x  7
3
5
x6
7
2
x  7 is _______________.
3
3
3
B) y  x  2
C) y   x  7
2
2
D) y 
5
x9
7
D) y 
2
x 1
3
1
x  3 and passing through (0, 0) has the equation ______.
2
1
1
B) y  x  6
C) y  2x
D) y  x  3
2
2
13. A line parallel to y 
A) y 
1
x
2
1
. The lines represented
3
by these equations are parallel. Which statement explains why this is true?
14. Consider the two equations: y  2x  3 and y  2x 
A) The coefficients of x in the two equations are the same because they have the same
slope.
B) The coefficients of y in the two equations are the same because they have the same
slope.
C) Both equations have two terms to the right of the equal sign.
D) The constants in the two equations are reciprocals and have opposite signs.
15. Which is the slope of a line perpendicular to the line 7 x  y  9 ?
1
1
A) -7
B)
C) 7
D) 
7
7
1
16. The line y   x  3 is perpendicular to which line?
2
1
1
A) y   x  6
B) y  2x  3
C) y  x  1
2
2
D) y  2x
17. A line perpendicular to y  4 x  2 is ________________.
1
A) y  4 x  2
B) y  x  1
C) y  4 x  2
4
D) y  
1
x 1
4
1
x  6 and y  5x  6 . The lines represented
5
by these equations are perpendicular. Which statement explains why this is true?
18. Consider the two equations: y 
A) The constants in the two equations are the same.
B) Both equations are written in slope-intercept form.
C) The coefficients of y in the two equations are the same because they have the same
slope.
D) The coefficients of x in the two equations are reciprocals and have opposite signs.
19. What best describes the relationship between the lines with equations y  2x  4
1
and y  2x  ?
4
A) perpendicular
B) parallel C) same line D) neither parallel nor perpendicular
20. What best describes the relationship between the lines with equations y  6   x
and y  x  6 ?
A) perpendicular
B) parallel C) same line D) neither parallel nor perpendicular
21. What best describes the relationship between the lines with equations y  3x  10
and 2y  6x  4 ?
A) perpendicular
B) parallel C) same line D) neither parallel nor perpendicular
22. What best describes the relationship between the lines with equations x  8y  8
and 16x  2y  0 ?
A) perpendicular
B) parallel C) same line D) neither parallel nor perpendicular
23. The admission cost to enter a fair is $5. The cost to ride each ride at the fair is
$1.50. Julie received a ½-off coupon that applies to the admission price. Julie decides
to graph the total cost on the y-axis and the number of rides on the x-axis, using the
equation y  1.50x  5 to represent the total cost, and the equation y  1.50 x  2.50
to represent the discounted cost. Which best describes the appearance of the
discounted cost line to that of the regular cost line?
A. less steep
B. more steep
C. same steepness, discounted cost line closer to the origin
D. same steepness, discounted cost line farther away from the origin
24. Line r is shown on the coordinate grid below.
Line q will also be shown on the grid. Line q has the same slope as line r and a yintercept that is greater than the y-intercept of line r. If the equations of the lines are
given in slope-intercept form, which statement about the equations must be true?
A. The constant for line q will be less than the constant for line r.
B. The constant for line q will be greater than the constant for line r.
C. The coefficient of x for line q will be less than the coefficient of x for line r.
D. The coefficient of x for line q will be greater than the coefficient of x for line r.
25. The power output of a new home solar power system was tracked for the last
several months. The output data are shown in the graph below.
The graph can be represented by the function p  100  80t . Which statement
describes how the line segment would change if the function was changed to
p  10  80t ?
A. The line segment would be flatter.
B. The line segment would move down 10 units.
C. The line segment would move down 90 units.
D. The line segment would slant down instead of up.
26. The net profit at the West City Hardware store over the last few months is shown
on the graph below.
If the coefficient of t were changed from -10 to 10 in the equation, how would this
change the graph of the equation?
A. The line segment would pass through the point (0, 10).
B. The line segment would pass through the point (0, 30).
C. The line segment would be flat or horizontal.
D. The line segment would be slanted up instead of down.
27. Line h is graphed on the coordinate plane below. The equation describing line h is
y  2x  2 .
How would the appearance of the graph change if the constant in the equation changed
to 2?
A. The line would slant the same and pass through the point (0, 2).
B. The line would slant the same and pass through the point (0, 0).
C. The line would be flatter and pass through the point (0, -2).
D. The line would slant upward and pass through the point (0, -2).
28. The graph of which equation has a steeper slope than the graph of y  2x  3 ?
A. y  2x  3
1
B. y   x  3
2
C. y  x  3
D. y  3x  3
29. Changing the coefficient of x in y  3x  2 from 3 to 1/3 has which effect on the
graph of the equation?
A. The line becomes less steep.
B. The line becomes more steep.
C. The line shifts down.
D. The line shifts up.