Grade 8 · Math

8th grade Linear, proportional or neither? worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Linear, proportional or neither?

Grade 8 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

Read this first
Use the table
input: folds output: layers rate from the row above, output change ÷ input change
0 1 –
1 2 1
2 4 2
3 8 4
1.
Bo folds a sheet of paper in half again and again and counts the layers. The third column shows each rate. Is it linear, proportional or neither?
- Proportional: every output is a whole number
- Neither: the rates are 1, 2 and 4
- Linear, not proportional: the rate is 1, and input 0 gives 1
2.
Every bag at the orchard stand holds 6 apples, and Jun fills the bags. Is the table linear, proportional or neither?
- Linear, not proportional: every rate is 6, but no row has input 0
- Neither: the outputs grow by 6, not by doubling
- Proportional: every rate is 6, and input 0 gives 0
3.
Luz measures a sunflower each week. It had a sunny week in the middle. Is the table linear, proportional or neither?
- Linear, not proportional: the rate is 3, and input 0 gives 10
- Proportional: input 0 gives 10
- Neither: the rates are 3, 4 and 3
4.
Pia sews square quilt patches and graphs each side against its area. Is the graph linear, proportional or neither?
- Proportional: the point (0, 0) is on the graph
- Proportional: the rate is 1, and input 0 gives 0
- Neither: the rates are 1, 3 and 5
5.
Ren tests the rule y = 4x + 1 by filling in x = 0, 1, 2 and 3. Is it linear, proportional or neither?
- Proportional: every rate is 4, so the line is straight
- Linear, not proportional: every rate is 4, but input 0 gives 1
- Neither: y is not 4 times x
6.
Tala tests the rule y = x × x by filling in x = 0, 1, 2 and 3. Is it linear, proportional or neither?
- Proportional: input 0 gives 0, and the outputs grow
- Proportional: the rate is 1, and input 0 gives 0
- Neither: the rates are 1, 3 and 5
7.
Zee tests the rule y = 2x + 6 by filling in x = 0, 1, 2 and 3. Is it linear, proportional or neither?
- Neither: the rule has two numbers in it, so it cannot be a straight line
- Proportional: every rate is 2, so the line is straight
- Linear, not proportional: every rate is 2, but input 0 gives 6
8.
Ari's plant is 5 cm tall when the class starts measuring. It grows 2 cm each week. Input: weeks. Output: height. Is it linear, proportional or neither?
- Linear, not proportional: 2 cm each week, but it is 5 cm at week 0
- Neither: it does not grow by doubling
- Proportional: it grows 2 cm every week, so the line is straight and steady
9.
Bo cuts paper squares with sides 1, 2 and 3 cm. Their areas are 1, 4 and 9 square cm. Input: side. Output: area. Is it linear, proportional or neither?
- Proportional: a 0 cm side gives 0 area, and the area grows
- Linear, not proportional: the area grows, but input 0 gives 1
- Neither: the area grows by 1, then 3, then 5
10.
Esme had read 30 pages of a book before Monday and then reads 15 pages each day. Input: days. Output: pages read. Is it linear, proportional or neither?
- Linear, not proportional: 15 pages each day, but it is 30 pages at day 0
- Neither: 30 pages is too many to start with
- Proportional: 15 more pages every day, so the line is straight

input: folds	output: layers	rate from the row above, output change ÷ input change
0	1	–
1	2	1
2	4	2
3	8	4

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

See all grade 8 math

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records