Dependent and independent variables worksheet

Grade 6 math, Common Core 6.EE.C.9. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Dependent and independent variables

Grade 6 math, Common Core 6.EE.C.9

Write an equation and name the independent and dependent variables.

1.
Write an equation for y in terms of x.
x 1 2 3 4
y 12 17 22 27
2.
Write an equation for y in terms of x.
x 1 2 3 4
y 6 12 18 24
3.
A plumber charges $84 per hour. Let h be the hours worked and c the total cost.
4.
Write an equation for y in terms of x.
x 1 2 3 4
y 7 9 11 13
5.
Write an equation for y in terms of x.
x 1 2 3 4
y 9 15 21 27
6.
A plumber charges $72 per hour. Let h be the hours worked and c the total cost.
7.
A plumber charges $50 per hour. Let h be the hours worked and c the total cost.
8.
Write an equation for y in terms of x.
x 1 2 3 4
y 11 15 19 23
9.
Write an equation for y in terms of x.
x 1 2 3 4
y 4 6 8 10
10.
Write an equation for y in terms of x.
x 1 2 3 4
y 7 12 17 22

x	1	2	3	4
y	12	17	22	27

x	1	2	3	4
y	6	12	18	24

x	1	2	3	4
y	7	9	11	13

x	1	2	3	4
y	9	15	21	27

x	1	2	3	4
y	11	15	19	23

x	1	2	3	4
y	4	6	8	10

x	1	2	3	4
y	7	12	17	22

Answer key: Dependent and independent variables

Grade 6 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. y = 5x + 7
y goes up by 5 each time x goes up by 1When x = 1, y = 12, so y = 5x + 7
2. y = 6x
y goes up by 6 each time x goes up by 1When x = 1, y = 6, so y = 6x
3. c = 84h. Independent: h (hours). Dependent: c (cost).
4. y = 2x + 5
y goes up by 2 each time x goes up by 1When x = 1, y = 7, so y = 2x + 5
5. y = 6x + 3
y goes up by 6 each time x goes up by 1When x = 1, y = 9, so y = 6x + 3
6. c = 72h. Independent: h (hours). Dependent: c (cost).
7. c = 50h. Independent: h (hours). Dependent: c (cost).
8. y = 4x + 7
y goes up by 4 each time x goes up by 1When x = 1, y = 11, so y = 4x + 7
9. y = 2x + 2
y goes up by 2 each time x goes up by 1When x = 1, y = 4, so y = 2x + 2
10. y = 5x + 2
y goes up by 5 each time x goes up by 1When x = 1, y = 7, so y = 5x + 2

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About dependent and independent variables

The independent variable is the one you choose or change, like the number of hours worked. The dependent variable depends on it, like the money earned. An equation such as e = 12h shows how the dependent variable changes when the independent one does.

Example 1

Eli earns $14 for each lawn mowed. Let L be the lawns mowed and e the money earned.

Answer: e = 14L. Independent: L (lawns). Dependent: e (earnings).

Example 2

A plant grows 6 centimeters each week. Let w be the number of weeks and g the growth in centimeters.

Answer: g = 6w. Independent: w (weeks). Dependent: g (growth).

Example 3

A plumber charges $67 per hour. Let h be the hours worked and c the total cost.

Answer: c = 67h. Independent: h (hours). Dependent: c (cost).

Watch out for

Ask “which one depends on the other?” The answer is the dependent variable.
The dependent variable usually goes alone on the left: c = 45h.
In a table, find how much y grows each time x goes up by 1. That is the number in front of x.

Practice dependent and independent variables online

On StudyWiz, your kid can practice dependent and independent variables with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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