Linear, proportional or neither?

Grade 8 Math Worksheet - Building Confidence

Circle the best answer.

1. Read this first

   Use the table

   input: week	output: height in cm	rate from the row above, output change ÷ input change
   0	4	–
   1	6	2
   2	8	2
   3	10	2

2. 1.

   Ari measures a bean sprout every week. The third column already shows each rate. Is it linear, proportional or neither?

   • Neither: input 0 gives 4, not 0
   • Linear, not proportional: every rate is 2, but input 0 gives 4
   • Proportional: every rate is 2, so the line is straight
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?

   • Neither: the rates are 2, 4 and 6
   • Proportional: the rate is 2, and input 0 gives 0
   • 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?

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

   Kira's bucket already has some water in it when the hose goes on. Is the table linear, proportional or neither?

   • Linear, not proportional: every rate is 2, but input 0 gives 3
   • Neither: all the outputs are odd numbers
   • Proportional: every rate is 2, so the line is straight
6. 5.

   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
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?

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

   Ren tests the rule y = 4x + 1 by filling in x = 0, 1, 2 and 3. Is it linear, proportional or neither?

   • Linear, not proportional: every rate is 4, but input 0 gives 1
   • Neither: y is not 4 times x
   • Proportional: every rate is 4, so the line is straight
10. 9.

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

    • Neither: the rates are 1, 3 and 5
    • Proportional: the rate is 1, and input 0 gives 0
    • Proportional: input 0 gives 0, and the outputs grow
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
    • Linear, not proportional: 2 cm each week, but it is 5 cm at week 0
    • Proportional: it grows 2 cm every week, so the line is straight and steady