Linear, proportional or neither?

Grade 8 Math Worksheet - Building Confidence

Circle the best answer.

1. 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

2. 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
3. 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
4. 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
5. 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
6. 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
7. 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
8. 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
9. 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
10. 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
11. 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