Grade 8 · Math

8th grade Linear, proportional or neither? worksheet

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Linear, proportional or neither?

Grade 8 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Read this first
Use the table
input: x output: y
1 4
3 10
3 11
5 16
0 1
1.
In math club, Tala gets a table where two rows were written for input 3. Is it linear, proportional or neither?
- Neither: input 3 has two different outputs
- Proportional: input 0 gives 1
- Linear, not proportional: every rate is 3, but input 0 gives 1
2.
Zee writes how many cups of flour go into different numbers of cookie batches. Is the table linear, proportional or neither?
- Linear, not proportional: every rate is 1 1/2, but no row has input 0
- Proportional: every rate is 1 1/2, and input 0 gives 0
- Neither: the outputs jump 4 1/2, 1 1/2 and 4 1/2
3.
Ari's math-club table looks steady at first glance. Is it linear, proportional or neither?
- Neither: the rates are 2, 2 and 5/2
- Proportional: every output is a whole number
- Linear, not proportional: the rate is 2, and input 0 gives 3
4.
Jun meets the rule y = x(x + 4) in math club. Is it linear, proportional or neither?
- Proportional: input 0 gives 0, and the outputs grow
- Neither: the rates are 5, 7 and 9
- Proportional: the rate is 5, and input 0 gives 0
5.
Kira meets the rule y = 3 − x ÷ 2 in math club and fills in x = 0, 2, 4 and 6. Is it linear, proportional or neither?
- Neither: the rule divides
- Linear, not proportional: every rate is -1/2, but input 0 gives 3
- Proportional: every rate is -1/2, so the line is straight
6.
Noah plots five points from the rule y = x × x × x. Is the graph linear, proportional or neither?
- Neither: the rates are 7, 1, 1 and 7
- Proportional: the point (0, 0) is on the graph
- Linear, not proportional: the points rise from left to right
7.
Ren lights a 30 cm candle. It burns down 1.5 cm each hour. Input: hours. Output: height. Is it linear, proportional or neither?
- Linear, not proportional: 1.5 cm less each hour, but it is 30 cm at hour 0
- Neither: 1.5 is not a whole number
- Proportional: it burns 1.5 cm every hour, so the line is straight and steady
8.
Zee's full water bottle holds 750 mL. On a hike, Zee drinks 125 mL each hour. Input: hours. Output: mL left. Is it linear, proportional or neither?
- Linear, not proportional: 125 mL less each hour, but it is 750 mL at hour 0
- Proportional: 125 mL gone every hour, so the line is straight
- Neither: the bottle will be empty after 6 hours
Use the table
input: x output: y
1 5
3 11
4 ?
7 23
Rows sorted by input.
Kira's math-club table is linear, but one output is missing. What output goes with input 4?
Milo's math-club table is linear, but one output is missing. What output goes with input 2?

input: x	output: y
1	4
3	10
3	11
5	16
0	1

input: x	output: y
1	5
3	11
4	?
7	23

8th grade Linear, proportional or neither? worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Linear, proportional or neither?. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can tell from a table, a graph, an equation or a story whether a relationship is linear: the rate (output change ÷ input change) is the same between every pair of rows.

Standard: 8.F.A.3 (also 8.EE.B.5)

Words to know

rate: Output change ÷ input change between two rows.

linear: Every pair of rows gives the same rate; the graph is a straight line.

proportional: Linear, and input 0 gives output 0: a straight line through (0, 0).

neither: Not linear (so not proportional either).

input step / output jump: How much the input goes up between two rows / how much the output changes.

step back: Use the rate to work out the row for input 0.

Common mistakes

Your child saw a steady rate and called the relationship proportional, but it does not start at 0.

Your child called a relationship proportional because it starts at 0, but its rate keeps changing.

Your child found the rate between the first two rows and stopped there, so a changing rate was missed. Try finding the change between every pair of rows together.

What to say

Ask: what is the amount at the very start, when the input is 0?

Ask: is the change the same every step?

Questions parents ask

What is the most common mistake with linear, proportional or neither??

Your child saw a steady rate and called the relationship proportional, but it does not start at 0.

How can I help my child with linear, proportional or neither??

Ask: what is the amount at the very start, when the input is 0?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

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