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Parallel and Perpendicular Lines/Equations

Total questions: 57

Worksheet time: 4hrs 12mins

Name
Class
Date
1.
Which figure shows a set of parallel lines?
a)
Figure 1
b)
Figure 2
c)
Figure 3
d)
Figure 4
2.

Are these line parallel or perpendicular?

a)

parallel

b)

perpendicular

3.

Are these line parallel or perpendicular?

a)

parallel

b)

perpendicular

4.
Which figure shows a set of perpendicular lines?
a)
Figure 1
b)
Figure 2
c)
Figure 3
d)
Figure 4
5.

Are these line parallel or perpendicular?

a)

parallel

b)

perpedicular

6.

Are these line parallel or perpendicular or neither?

a)

parallel

b)

neither

c)

perpendicular

7.
Slopes of parallel lines are...
a)
opposite reciprocals.
b)
opposites.
c)
the same.
d)
always 7.
8.
Slopes of perpendicular lines are...
a)

opposite reciprocals (flip fraction)

b)
opposites.
c)
the same.
d)
always 7.
9.
y = 3x +2
y = 3x - 3
These lines are...
a)
Parallel
b)
Perpendicular
c)
Neither
d)
The same line
10.
y = -2/3x + 2
y = 3/2x + 9
These lines are...
a)
Parallel
b)
Perpendicular
c)
Neither
11.

Choose the linear equation that is parallel to the following line

y=−14x−1y=-\frac{1}{4}x-1  

a)

y=−14x+5y=-\frac{1}{4}x+5  

b)

y=14x−1y=\frac{1}{4}x-1  

c)

y=−4x−1y=-4x-1  

d)

y=41x−1y=\frac{4}{1}x-1  

12.

Choose the linear equation that is perpendicular to the following line

y=−14x−1y=-\frac{1}{4}x-1  

a)

y=−14x+5y=-\frac{1}{4}x+5  

b)

y=14x−1y=\frac{1}{4}x-1  

c)

y=−4x−1y=-4x-1  

d)

y=41x−3y=\frac{4}{1}x-3  

13.

y = 5x + 1
y = 5x - 4
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

d)

The same line

14.

y = 6x + 2

y = -6x + 2

These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

15.

y = -2/3x + 2

y = 3/2x + 9

These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

16.

y = 3x + 2
y = 3x - 5
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

d)

The same line

17.

y = 4/5x - 3

y = -5/4x + 7

These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

18.

y = 4/5x - 3

y = 4/5x + 7

These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

19.

y = 1/2x + 3

y = -2/1x - 5

These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

20.

y = 8x + 1

y = -9x + 2

These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

21.
There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?
a)
x + y = 15
4x + 2y = 44
b)
4x + 2y = 15
x + y = 44
c)
x = 2y + 44
4x = y + 15
d)
2x - 4y = 44
x - y = 15
22.

Solve this system of equations by graphing.

y = 1/2x + 2

y = -3x + 9

a)

(2, 3)

b)

(-2, -3)

c)

(3, 2)

d)

(-3, 2)

23.
What is the solution to this system?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
24.
When you graph the exact same equation twice,
a)
you will have no solution. 
b)
you will have one solution.
c)
you will have infinite solutions. 
d)
you will graph a giraffe. 
25.
How many solutions will this system have? 
a)
No solution
b)
One Solution
c)
I Don't Know
d)
Infinitely Many Solutions
26.
If a system of linear equations has one solution, what does this mean about the two lines? 
a)
Parallel lines
b)
the same line 
c)
Intersecting lines
27.
If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 
a)
Intersecting lines
b)
Same line
c)
Parallel lines
28.
Solve the system by graphing:
y = 6x - 4
y = -x + 3
a)
(1, 2)
b)
(2, 1)
c)
(4, 5)
d)
(2, 4)
29.
What is the solution to the system?
a)
(3, -1)
b)
(2, -6)
c)
No Solution 
d)
(6, -2)
30.
Lesly graphed two lines in order to find the solution to a given system of equations.
What is the solution?
a)
(-3,-8)
b)
(-8,-3)
c)
(3,-8)
d)
(8,3)
31.
Graph both equations. What point do they intersect at?
y = 2x
y = 3x + 1
a)
(-1, -2)
b)
(2, 1)
c)
(2, 4)
d)
(-2, -3)
32.
Graph both equations. What point do they intersect at?
y = x + 3
y = -x - 1
a)
(1, 3)
b)
(-1, 0)
c)
(-2, 1)
d)
(3, -1)
33.
Graph both equations. What point do they intersect at?
y = x
y = -x
a)
(1, 1)
b)
(0, 0)
c)
(2, 2)
d)
(1, -1)
34.
Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat.  Write an equation for C, the total cost, to rent the boat for h hours.
a)
h = 2C + 15
b)
C = 15h + 2
c)
h = 15C + 2
d)
C = 2h + 15
35.
Solve by elimination 
5x+6y= -10
3x-2y= -6
a)
(-2,0)
b)
(0,-2)
c)
(2,0)
d)
(0,2)
36.
What is the solution to this system?
y = 2x + 1
y = 4x - 1
a)
(1,3)
b)
(-1,-3)
c)
(-1,3)
d)
(3,1)
37.
What is the solution to this system?
y = 2/3x - 2
y = -x + 3
a)
(0,3)
b)
(0,-3)
c)
(3,0)
d)
(-3,0)
38.
What is the solution to this system?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
39.
What is the solution to this system?
a)
One Solution
b)
No solution
c)
Infinitely Many Solutions
40.
Parallel Lines never intersect because...
a)
they have the same slopes. 
b)
they have the same y-intercept.
c)
they have different slopes.
d)
they have different y-intercepts. 
41.
Find the slope of the line.
a)
-2
b)
2
c)
-1
d)
1
42.
What type of slope?
a)
negative
b)
steep
c)
undefined
d)
zero slope
43.
There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?
a)
x + y = 15
4x + 2y = 44
b)
4x + 2y = 15
x + y = 44
c)
x = 2y + 44
4x = y + 15
d)
2x - 4y = 44
x - y = 15
44.

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

a)

4x + 6y = 3

13.5x - 13y = 6

b)

x + y = 4

x - y = 6

c)

4x + 6y = 13

3x + 7y = 13.5

d)

4x - 6y = 13

3x - 7y = 13.5

45.

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?

a)

x + y = 1430

20x + 50y = 49

b)

x + y = 49

10x + 5y = 1430

c)

x + y = 49

20x + 50y = 1430

d)

x + y = 49

x + y = 1430

46.
There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?
a)
x + y = 15
4x + 2y = 44
b)
4x + 2y = 15
x + y = 44
c)
x = 2y + 44
4x = y + 15
d)
2x - 4y = 44
x - y = 15
47.
The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?
a)
S + A = 530
3S + 4A = 1740
b)
S + A = 530
4S + 3A = 1740
c)
S + A = 1740
3S + 4A = 530
d)
S + A = 1740
4S + 3A = 530
48.

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

a)

t + n = 54

t = 3n + 8

b)

t + n = 54

n = 3t + 8

c)

t + n = 54

t = 3n - 8

49.

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

a)

t + n = 54

t = 3n + 8

b)

t + n = 54

n = 3t + 8

c)

t + n = 54

t = 3n - 8

d)

t + n = 8

t = 3n + 54

50.

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

a)

1.5N+0.5S=78.5

N+S=87

b)

1.5N+0.5S=78.5

1.5N+0.5S=87

c)

N+S=78.5

1.5N+0.5S=87

d)

N+S=78.5

N+S=87

51.
Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?
a)
4x + 6y = 3
13.5x - 13y = 6
b)
x + y = 4
x - y = 6
c)
4x + 6y = 13
3x + 7y = 13.5
d)
4x - 6y = 13
3x - 7y = 13.5
52.

The senior class at Rivermont High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Washington High School rented and filled 12 vans and 14 buses with 770 students. Which system of equations solves this problem to show how many students were in each van and each bus?

a)

11v + 3b = 283

12v + 14b = 770

b)

v + b = 14

v + b = 16

c)

11v + 12v = 283

3b + 14b = 770

d)

v + b = 30

23v + 17b = 1053

53.
On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 
a)
10c + 5d = 14.25
5c + 10d = 16.50
b)
10c + 5d = 16.50
5c + 10d = 14.25
c)
c + d = 10
5c + 10d = 16.50
d)
c + d = 5
5c + 10d = 16.50
54.
Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? 
a)
x + y = 6
14.80x + 17y = 91
b)
x + y = 91
14.80x + 17y = 6
c)
x + y = 6
14.80y + 17x = 91
d)
x + y = 91
14.80x+ 17y = 6
55.
Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? 
a)
x + y = 1550
y  = 4x
b)
x + y = 1550
y = x + 4
c)
y - x = 1550
y = 4x
d)
y = 1550 + x
y = x + 4
56.

A jar contains only nickels and quarters. The total number of coins in the jar is 15. The total value of the coins is $2.35. Which system of equations represents this situation?

a)

n + q = 2.35

.05n + .25q = 15

b)

n + q = 15

.5n + .25q = 15

c)

n + q =15

.05n + .25q = 2.35

d)

.05n + q = 15

n + .25q = 2.35

57.
Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.
a)
x + y = 33
y = 2x - 3
b)
x + y = 33
x = 2y - 3
c)
x + y = 33
x = 3 - 2y
d)
x + y = 3
x = 33 - 2y

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