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.

   In math club, Esme copies a mystery table from the board. The third column shows each rate. Is it linear, proportional or neither?

   • Proportional: the rate is 2, and input 0 gives 0
   • Neither: the rates are 2, 4 and 6
   • Proportional: input 0 gives 0, and the outputs grow
4. 3.

   Every bag at the orchard stand holds 6 apples, and Jun fills the bags. Is the table linear, proportional or neither?

   • Neither: the outputs grow by 6, not by doubling
   • Proportional: every rate is 6, and input 0 gives 0
   • Linear, not proportional: every rate is 6, but no row has input 0
5. 4.

   Luz measures a sunflower each week. It had a sunny week in the middle. Is the table linear, proportional or neither?

   • Proportional: input 0 gives 10
   • Neither: the rates are 3, 4 and 3
   • Linear, not proportional: the rate is 3, and input 0 gives 10
6. 5.

   Milo lets out kite string at a steady speed and graphs it, starting the graph at second 1. Is it linear, proportional or neither?

   • Linear, not proportional: every rate is 3, but no point has input 0
   • Proportional: every rate is 3, and input 0 gives 0
   • Neither: the line goes up too fast
7. 6.

   Noah's toy car rolls along a track that starts at the 4 m mark. Is the graph linear, proportional or neither?

   • Neither: the line does not start at 0
   • Proportional: every rate is 3, so the line is straight
   • Linear, not proportional: every rate is 3, but input 0 gives 4
8. 7.

   Pia sews square quilt patches and graphs each side against its area. Is the graph linear, proportional or neither?

   • Proportional: the rate is 1, and input 0 gives 0
   • Proportional: the point (0, 0) is on the graph
   • Neither: the rates are 1, 3 and 5
9. 8.

   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
10. 9.

    Zee tests the rule y = 2x + 6 by filling in x = 0, 1, 2 and 3. Is it linear, proportional or neither?

    • Proportional: every rate is 2, so the line is straight
    • Neither: the rule has two numbers in it, so it cannot be a straight line
    • Linear, not proportional: every rate is 2, but input 0 gives 6
11. 10.

    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?

    • Neither: it does not grow by doubling
    • Proportional: it grows 2 cm every week, so the line is straight and steady
    • Linear, not proportional: 2 cm each week, but it is 5 cm at week 0