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?

   • Linear, not proportional: every rate is 2, but input 0 gives 4
   • Neither: input 0 gives 4, not 0
   • Proportional: every rate is 2, so the line is straight
3. 2.

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

   • Proportional: every rate is 6, and input 0 gives 0
   • Neither: the outputs grow by 6, not by doubling
   • Linear, not proportional: every rate is 6, but no row has input 0
4. 3.

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

   • Neither: all the outputs are odd numbers
   • Linear, not proportional: every rate is 2, but input 0 gives 3
   • Proportional: every rate is 2, so the line is straight
5. 4.

   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
6. 5.

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

   • Proportional: every rate is 3, so the line is straight
   • Linear, not proportional: every rate is 3, but input 0 gives 4
   • Neither: the line does not start at 0
7. 6.

   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
8. 7.

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

   • 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
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?

    • Proportional: 15 more pages every day, so the line is straight
    • Neither: 30 pages is too many to start with
    • Linear, not proportional: 15 pages each day, but it is 30 pages at day 0