Free Printable Writing Equations/ Inequalities & Direct Variation

1.

The 30 members of a choir are trying to raise $1500 to cover travel costs to a singing camp. They have already raised $600. Which equation would you solve to find the average amount each member can raise in order to meet the goal?

a)

30x + 600 = 1500

b)

30x - 600 = 1500

c)

x + 600 = 1500

d)

30x = 1500

2.

Mr. Piper's plumbing needed repairs. The plumber charged $98 for parts plus $45 per hour for labor. If the bill totaled $458, how could I find out the hours of labored required?

a)

98x + 45 = 458

b)

98 + 45x = 458

c)

45 + 98 = 458

d)

45x - 98 = 458

3.

Pizzazz Publications is having some books printed. The printer charges $800 plus $5 per book. What equation could help me find how many books can be printed for $4,000?

a)

800 + 5x = 4000

b)

800x + 5 = 4000

c)

4000 + 5x= 800

d)

800 + 5 = 4000

4.

Mei was going to sell all of her stamp collection to buy a video game. After selling half of them she changed her mind. She then bought nineteen more. How many did she start with if she now has 45?

a)

2/x + 19 = 90

b)

x/2 + 19 = 45

c)

2x +19 = 109

d)

19x + 2 = 71

5.

At Joe's Clown Car Rental Agency, renting a car costs $35 plus $0.75 for every mile it is driven. What is an equation that can be used to find the number of miles, m, a vehicle was driven, if the total rental charge was $222.50?

a)

222.5 = m(35 + 0.75)

b)

222.5 = 35 + 0.75m

c)

222.5 = 0.75 + 35m

d)

222.5 = 0.75(m + 35)

6.

Dexter's Gym charges a one-time registration fee of $40 and $20 each month. The total fee after x months is $340. Which equation models this situation?

a)

40x + 20 = 340

b)

20x + 40 = 340

c)

20x - 40 = 340

d)

20 + 340 = 40x

7.

Scott's Automotive charges $35 for each car plus $7 per hour. Write an equation that represents this scenario if Kylie was charged $63.

a)

35x + 7 = 63

b)

7x = 63

c)

7x - 35 = 63

d)

7x + 35 = 63

8.

You and your friends plan to attend the county fair this weekend. Admission to the fair is $5 and the cost per ride is $0.50. How many rides can you go on if you have $20?

a)

20 rides

b)

30 rides

c)

40 rides

d)

50 rides

9.

Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. Write an equation that represents this scenario if she spends $35 in all.

a)

.50x + 20 = 35

b)

.50x = 35

c)

.50 + 20x = 35

d)

.50x - 20 = 35

10.

Mallory bought pizza and soda for her End of Summer party. If she spent $12.57 on the sodas and $10.95 for each pizza, how many pizzas did she buy if she spent $89.22? Which equation models this scenario?

a)

10.95x + 12.57 = 89.22

b)

89.22x - 10.95 = 12.57

c)

12.57x + 10.95 = 89.22

d)

12.57 + 10.95 = 89.22

11.

Write a linear equation in the form of (a)

Choose from the below words

y = 2x + 3

y = -2x + 3

y = 2x -3

y = 3x - 4

12.

Write a linear equation in the form of y=mx+b

a)

y= 3x + 5

b)

y = 5x - 3

c)

y = 2x + 3

d)

y = 5x + 3

13.

Write a linear equation in the form of y=mx+b

a)

y = 2x + 2

b)

y = 2x - 2

c)

y = x + 2

d)

y = 3x - 2

14.

a)

y = –2x + 2

b)

y = –2x + 2

c)

y = –2x – 2

d)

y = 2x – 2

15.

a)

y = –11x + 5

b)

y = 11x + 5

c)

y = –5x – 11

d)

y = 5x – 11

16.

Write the exponential equation that represents the given table.

a)

$y=80\cdot4^x$

b)

$y=80\cdot\frac{1}{4}^x$

c)

$y=80-60x$

d)

$y=80+\frac{1}{4}x$

17.

Write the exponential equation that represents the given table.

a)

$y=5\cdot2^x$

b)

$y=10\cdot2^x$

c)

$y=5+2x$

d)

$y=10x+10$

18.

Write the exponential equation that represents the given table.

a)

$y=21\cdot3^x$

b)

$y=7+3x$

c)

$y=7\cdot3^x$

d)

$y=21-42x$

19.

Write the exponential equation that represents the given table.

a)

$y=2\cdot1^x$

b)

$y=1x+2$

c)

$y=2+1.5x$

d)

$y=2\cdot1.5^x$

20.

Write the exponential equation that represents the given graph.

a)

$y=12-0.5x$

b)

$y=12\cdot0.5^x$

c)

$y=12\cdot2^x$

d)

$y=12-6x$

21.

Write the quadratic equation to model the table of values. $y=ax^2+bx+c$

Step 1: "c" is your y-intercept

Step 2: "a" is your 2nd level difference $\div$ 2

Step 3: Select an (x,y) coordinate other than the y-int

Step 4: Plug all these value into the equation and solve for "b"

Step 5: Now you know "a", 'b", and "c"...Plug into the original equation.

a)

$y=4x^2+7x+8$

b)

$y=2x^2+2x-2$

c)

$y=x^2+7x+8$

22.

Which function best best models the data?

a)

F

b)

G

c)

H

d)

J

23.

Which function best models the data?

a)

A

b)

B

c)

C

d)

D

24.

Which function best models the data?

a)

A

b)

B

c)

C

d)

D

25.

Which function can best be used to model this situation?

a)

A

b)

B

c)

C

d)

D

26.

What is the equation of this line?

a)

0

b)

undefined

c)

y = -2

d)

x = -2

27.

Give the equation for the graph

a)

y = 5x - 3

b)

y = 4x + 2

c)

y =-2x + 5

d)

y = - 2x + 4

28.

The graph represents the height of a burning candle. What is the meaning of the y-intercept?

a)

the time it takes to burn the entire candle

b)

the rate at which the candle is losing height

c)

the change in the height of the candle each hour

d)

the original height of the candle

29.

Charlie rented a moving truck. He paid a daily fee plus a per-mile fee to rent the truck. The equation below represents the daily amount Charlie paid for the truck if he drives it x miles.
y=0.5x+10
What does the slope of the graph of this equation represent?

a)

The daily fee for the moving truck

b)

The per-mile fee for the moving truck

c)

How much Charlie paid for the truck

d)

The number of miles he drove

30.

What is the equation of the linear function?

a)

y = -3x + 10

b)

y = -3x + 16

c)

y = 3x + 10

d)

y = 3x + 16

31.

Graph. x = 1

a)

a

b)

b

c)

c

d)

d

32.

Graph. y = 2/5x

a)

a

b)

b

c)

c

d)

d

33.

Given the table, write the equation in the slope-intercept form.

a)

y = 1/3x + 6

b)

y = 3x + 6

c)

y = 2x + 6

d)

y = 1/2x + 6

34.

What is the equation of the line?

a)

y = -3/4x + 3

b)

y = 4/5x + 3

c)

y = -4/5x + 3

d)

y = -4/5x

35.

a)

A

b)

B

c)

C

d)

D

36.

Write the equation of the line.

a)

y = -1/3x - 2

b)

y = 1/3x - 2

c)

y = 3x - 2

d)

y = -3x - 2

37.

What is the equation for this table?

a)

y = -2x + 5

b)

y = 2x + 5

c)

y = 5x - 2

d)

y = 5x + 5

38.

What is the equation of this line?

a)

x=-2

b)

y=-2x

c)

x=2

d)

y=-2

39.

Which of these tables of values satisfy the equation y = 2x + 3?

a)

C

b)

D

40.

Which equation matches the table?

a)

y = 1.5x + 1

b)

y = 0.5x + 1

c)

y = x + 1.5

d)

y = x

41.

Johnny has to pay $15 for a large pizza and 1.50 for each topping. What is the meaning of the y-intercept?

a)

It cost 1.50 per topping

b)

It cost 1.50 for unlimited toppings

c)

It cost $15 for a large pizza

d)

It cost $15 for a large pizza with no toppings

42.

The graph represents the money in a savings account. What is the meaning of the y-intercept?

a)

The initial deposit was $30

b)

$30 is added to the account each week

c)

It took 30 weeks to same enough money to open an account

d)

not enough information

43.

Dona plays a game with her brother. The both start with 75 points. For each round that they win, they receive 30 points. The equation that models each person's score is
y = 30 x + 75, where x is the number of games a person wins. What is the meaning of the slope?

a)

the number of games won

b)

the amount of points that a player begins with

c)

the change in points for each game a person wins

d)

the number of points needed to win the game

44.

What is the meaning of the slope?

a)

The cost for the service without any hours of calling is $5

b)

The cost of the service without any hours of calling is $6

c)

The cost per minute is $0.05

d)

The cost per minute is $0.50

45.

Rich is a member of a gym. He pays a monthly fee plus a per-visit fee. The equation below represents the monthly amount Rich pays for his membership to the gym per month for x visits.
y=3x+10
What does the y-intercept of the graph of this equation represent?

a)

The monthly fee

b)

How much Rich pays per visit

c)

The number of times Rich goes to the gym

d)

The total cost at the end of the month

46.

Which equation matches the table?

a)

y = x + 5

b)

y = 5x

c)

y = x - 5

d)

x = y - 5

47.

What is the algebraic equation for this table?

a)

y = x + 3

b)

y = 3x

c)

y = x ÷ 3

d)

y = x - 3

48.

Which equation matches the table?

a)

y = x

b)

y = 5x

c)

y = x - 4

d)

y = x + 4

49.

Which equation matches the table?

a)

y = 3x + 9

b)

y = 1/3x + 9

c)

y = x + 3

d)

y = 12x - 3

50.

Which equation best represents the relationship between x and y in the table shown?

a)

y = -3x - 10

b)

y = -1/3x - 10

c)

y = 3x + 10

d)

y = 3x - 10

51.

What is the equation of the linear function?

a)

y = -3x + 10

b)

y = -3x + 16

c)

y = 3x + 10

d)

y = 3x + 16

52.

What is the function of the table?

a)

y=3x+1

b)

y=4x-2

c)

y=x+1

d)

y=x+7

53.

Given the table, write the equation in the slope-intercept form.

a)

y = 1/3x + 6

b)

y = 3x + 6

c)

y = 2x + 6

d)

y = 1/2x + 6

54.

Which equation best represents the relationship between x and y in the table shown?

a)

y= 5x+5

b)

y=1/5x+5

c)

y=15x+5

d)

y=10x+5

55.

Given the two points: (0, 6) and (6,18), write the equation of the line in point-slope form.

a)

$y-18=2\left(x-6\right)$

b)

$y-18=\frac{1}{2}\left(x+6\right)$

c)

$y+18=2\left(x+6\right)$

d)

$y+18=\frac{1}{2}\left(x+6\right)$

56.

Write an equation of the line that passes through (0 , 10) and (6 , 34)

a)

y = 4x + 10

b)

y = 6x + 34

c)

y = 4

d)

y = 6x - 4

57.

Write the linear equation in y = mx + b form using the given points.

a)

y = -2x + 1

b)

y = -3x + 1

c)

y = 2x + 1

d)

y = 3x - 1

58.

A man is climbing down from 100 feet high descending 30 feet per minute.

a)

y = 100 - 30x

b)

y = 100 + 30x

c)

y = 100x + 30

d)

y = 100x - 30

59.

A holiday meal cost $12.50 a person plus a delivery fee of $30. Which equation represents the amount a holiday meal costs(y), including delivery, for x people?

a)

y = 12.50 + 30x

b)

y = 30 + 12.50x

c)

y = 12.50 + 30

d)

12.50x = 30

60.

What is the equation for this graph?

a)

y = ⅔ x + 3

b)

y = -⅔ x + 3

c)

y = ⅔ x - 3

d)

y = -⅔ x - 3

61.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

62.

Write the equation of the line in point-slope form by using the given point.

a)

$y-3=3\left(x+2\right)$

b)

$y+3=-3\left(x-2\right)$

c)

$y+3=-\frac{1}{3}\left(x-2\right)$

d)

$y-3=-3\left(x+2\right)$

63.

Write the equation of this graph in standard form.

a)

$-\frac{1}{2}x+y=-3$

b)

$2x+y=-3$

c)

$-2x+y=-3$

d)

$\frac{1}{2}x+y=3$

64.

Which equation matches this table?

a)

$x+y=8$

b)

$-\frac{1}{2}x+y=9$

c)

$2x+y=8$

d)

$\frac{1}{2}x+y=9$

65.

What is the equation of the linear function?

a)

y = -3x + 10

b)

y = -3x + 16

c)

y = 3x + 10

d)

y = 3x + 16

66.

Mr. Newman's class needs to sell at least 70 tickets for the school's car wash for them to raise money for their class t-shirt. Morning tickets cost $4 and afternoon tickets cost $6. If their goal is to raise more than $450, which system of inequalities can be used to determine the number of morning tickets, m, and afternoon tickets, a, they need to sell?

a)

$m+a\le70$

$4m+6a\le450$

b)

$m+a\le450$

$4m+6a\le70$

c)

$m+a\ge70$

$4m+6a\ge450$

d)

$m+a\ge450$

$4m+6a\ge70$

67.

Steven wants to buy chocolate bars and lollipops. Each chocolate bar costs $5 and the lollipops cost $6. If Steven can spend at most $90 and can only buy less than 13 items, which inequality best models this situation?

a)

$c+l>13$

$5c+6l\le90$

b)

$5c+6l\le13$

$c+l<90$

c)

$c+l<13$

$5l+6c\le90$

d)

$c+l<13$

$5c+6l\le90$

68.

Match the following words to its corresponding inequality symbol.

a)

$\ge$

1.

at least

b)

$>$

2.

more than

c)

$<$

3.

less than

d)

$\le$

4.

maximum

69.

Match the following words to its corresponding inequality symbol.

a)

$\le$

1.

at most

b)

$>$

2.

above

c)

$\ge$

3.

or more

d)

$<$

4.

below

70.

A boy has seven more nickels than quarters. The total value of the coins is $4.90. Which system could be used to find out how many nickels and quarters he has?

a)

b)

c)

d)

71.

Write an equation of a line in point-slope form with a slope of 6 that goes through (11, 5).

a)

y-5=6(x-11)

b)

y-11=6(x-5)

c)

y+5=6(x+11)

d)

y+11=6(x+5)

72.

Which of these represents point-slope form of a linear equation?

a)

y - y₁ = m(x - x₁)

b)

Ax + By = C

c)

y = mx + b

73.

Write the equation in point-slope form of the line that passes through the given point and has the given slope.
(4, -7); m = -1/4

a)

y +7 = -1/4(x - 4)

b)

y - 4 = -1/4(x + 7)

c)

y+ 7 = 4(x - 4)

d)

y - 7 = -1/4(x - 4)

74.

Write the equation in point-slope form of the line that passes through the given point and has the given slope:
(-2, -1); m= -3

a)

y + 1 = -3(x - 2)

b)

y + 1 = -3(x + 2)

c)

y - 1 = 3(x - 1)

d)

y + 2 = -3(x + 1)

75.

Which equation is written in STANDARD form?

a)

y = 1/2x + 2

b)

y - 3 = -5(x + 2)

c)

-7x + 2y = 9

d)

3x + 2 = y

76.

Write the standard form of the equation for the line:

4y = x + 4

a)

x + 4y = 8

b)

-x + 4y = -16

c)

y = x + 16

d)

4y + x = 8

77.

Rewrite in standard form. Do not use spaces at all in your answer.

7x=2y+9

(a)

78.

Rewrite in standard form. Do not use spaces at all in your answer.

2x=\frac{y}{2}-4

(a)

79.

Write the equation for the line passing through the point (4, 2) with a slope of ¼.

a)

y = ¼x + 2

b)

y = ¼x + 4

c)

y = ¼x + 1

d)

y = ¼x + 3.5

80.

Write an equation in standard form that passes through (6, 11) and (5, 9).

a)

2x - y = 1

b)

2x + y = 19

c)

2x + y = 23

d)

x - 2y = -16

81.

Write in slope intercept form
5x - 3y = -9

a)

y = (5/3)x - 3

b)

y = (5/3)x + 9

c)

y = (5/3)x + 3

d)

y = (3/5)x + 3

82.

Write the equation in point-slope form of the line that passes through the given point and has the given slope.
(4, -7); m = -1/4

a)

y +7 = -1/4(x - 4)

b)

y - 4 = -1/4(x + 7)

c)

y+ 7 = 4(x - 4)

d)

y - 7 = -1/4(x - 4)

83.

Write in standard form.
4y - 3 = 6x + 6

a)

6x - 4y = -9

b)

6x - 4y = 3

c)

4y - 6x = -9

d)

4x + 4y = 3

84.

Write the equation of the line in POINT-SLOPE FORM given 2 points.

a)

a

b)

b

c)

c

d)

d

85.

Write the equation of the line in SLOPE-INTERCEPT FORM given the equation:

a)

a

b)

b

c)

c

d)

d

86.

Rewrite to slope intercept form.
y - 4 = 2(x + 6)

a)

y = 2x + 10

b)

y = 2x + 8

c)

y = 2x + 16

d)

y = 2x + 20

87.

A motel is purchasing new towels. Suites require 12 towels and individual rooms require 5 towels. The minimum order required by the towel vendor is 651 towels.

a)

12s + 5t < 651

b)

12s + 5t > 651

c)

12s + 5t > 651

d)

12s + 5t < 651

88.

The Shoemaker Movie Theater is selling tickets to a new movie. Adult tickets cost $12 and child tickets cost $7. The goal is to sell at least $1000 worth of tickets for the Shoemaker Theater.

a)

12a + 7c < 1000

b)

12a + 7c < 1000

c)

12a + 7c > 1000

d)

12a + 7c > 1000

89.

Derek is purchasing hammers and wrenches for his workshop, and he would like to spend under $120. Each hammer costs $10, and each wrench costs $7.

a)

10h + 7w < 120

b)

12h + 7w < 120

c)

12h + 7w > 120

d)

12h + 7w > 120

90.

Anthony is purchasing dried apricots and cherries to use in his homemade trail mix, which requires at least 235 grams of fruit in total. Each dried apricot weighs 6 grams and each dried cherry weighs 1 gram

a)

6a + 1c < 235

b)

6a + 1c < 235

c)

6a + 1c > 235

d)

6a + 1c > 235

91.

Angel is building a shelving unit to hold all of his shoes. A pair of Lebrons takes up 1 square foot of space, and a pair of Tims occupies 3 square feet. The total amount of shelving taken up by all the shoes can be at most 46 square feet.

a)

1l + 3t < 46

b)

1l + 3t < 46

c)

1l + 3t > 46

d)

1l + 3t > 46

92.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

_D

93.

Which of the following equations match the given graph?

a)

y ≤ -3/4 x + 3

b)

y ≥ -3/4 x + 3

c)

y < -3/4 x + 3

d)

y > -3/4 x + 3

94.

Which of the following equations match the given graph?

a)

x ≥ -1

b)

x ≤ -1

c)

x > -1

d)

x < -1

95.

Which point below is NOT a part of the solution set?

a)

(0, 0)

b)

(0, 1)

c)

(-100, -3)

d)

(5, 10)

96.

Determine the equation of the line.

a)

$y=4x+3$

b)

$y=3x+4$

c)

$y=-4x-1$

d)

$y=-3x-1$

97.

Determine the equation of the line.

a)

$y=-\frac{1}{5}x+2$

b)

$y=5x+2$

c)

$y=\frac{1}{5}x-2$

d)

$y=5x-2$

98.

Write the slope-intercept form of the equation of the line through the following points: $\left(-1,\ 7\right)\ and\ \left(3,\ -5\right)\$

a)

$y=-3x+4$

b)

$y=4x-3$

c)

$y=-\frac{1}{3}x-4$

d)

$y=-\frac{1}{4}x+4$

99.

Write the slope-intercept form of the equation of the line through the given point with the given slope:
$through\ \left(-1,\ -5\right);\ slope=8$

a)

$y=-x+8$

b)

$y=8x-1$

c)

$y=8x+3$

d)

$y=3x+8$

100.

Eduardo counted ten seconds between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles away. What is the constant of variation?

a)

k = 10

b)

k = 2

c)

k = 5

d)

k = 1/5

101.

Eduardo counted ten seconds between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles away. What is the equation of variation?

a)

y = 10x

b)

y = 2x

c)

y = 5x

d)

y = 1/5x

102.

Eduardo counted ten seconds between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles away. If he counted four seconds between the next flash of lightning and thunder, about how far away was the lightning?

a)

40 miles

b)

4/5 miles

c)

8 miles

d)

20 miles

103.

A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00 for 20 hours of work. What is the constant of variation?

a)

k = 123

b)

k = 20

c)

k = 6.15

d)

k = 0.16

104.

A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00 for 20 hours of work. What is the equation of variation?

a)

y = 123x

b)

y = 20x

c)

y = 6.15x

d)

y = 0.16x

105.

A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00 for 20 hours of work. Find the amount of pay for 31 hours of work.

a)

$3813

b)

$620

c)

$190.65

d)

$4.96

106.

At top speed, a rabbit can cover 7 miles in 12 minutes. What is the constant of variation?

a)

k = 7

b)

k = 12

c)

k = 12/7

d)

k = 7/12

107.

At top speed, a rabbit can cover 7 miles in 12 minutes. What is the equation of variation?

a)

y = 7x

b)

y = 12x

c)

y = 12/7x

d)

y = 7/12x

108.

At top speed, a rabbit can cover 7 miles in 12 minutes. If a rabbit could continue at this rate indefinitely, how long would it take the rabbit to cross the 220-mile expanse of the Mojave Desert?

a)

31.4 minutes

b)

18.3 minutes

c)

377.1 minutes

d)

128.1 minutes

109.

A dishwasher uses 65 gallons of water to wash 5 loads of dishes. What is the constant of variation?

a)

k = 13

b)

k = 65

c)

k = 5

d)

k = 1/13

110.

A dishwasher uses 65 gallons of water to wash 5 loads of dishes. What is the equation of variation?

a)

y = 13x

b)

y = 65x

c)

y = 5x

d)

y = 1/13x

111.

A dishwasher uses 65 gallons of water to wash 5 loads of dishes. How many gallons of water would be used to wash 12 loads?

a)

60 gallons

b)

780 gallons

c)

156 gallons

d)

12/13 gallons

Writing Equations/ Inequalities & Direct Variation

Total questions: 111

Worksheet time: 6hrs 33mins

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