Linear, proportional or neither?

Answer Key - Grade 8 Math Worksheet

Circle the best answer, or write your answer on the line.

1. Read this first

   Use the table

   input: hours after lighting	output: height in cm
   4	12
   1	18
   3	14
   6	8

2. 1.

   Kira measures a candle at a few hours after it is lit. Is the table linear, proportional or neither?

   • Neither: the outputs jump -4, -2 and -4
   • Proportional: every rate is -2, so the line is straight
   • Linear, not proportional: every rate is -2, but input 0 gives 20
3. 2.

   Milo's math-club table has no row for input 0. Is it linear, proportional or neither?

   • Proportional: every rate is -2, and input 0 gives 0
   • Linear, not proportional: every rate is -2, but no row has input 0
   • Neither: the outputs jump -6, -4 and -2
4. 3.

   Pia plots four points from a rule card in math club. Is the graph linear, proportional or neither?

   • Neither: some outputs are negative, so a straight line cannot fit them
   • Linear, not proportional: every rate is 3, but input 0 gives -1
   • Proportional: every rate is 3, so the line is straight
5. 4.

   Ren plots four points from a rule card, but none of them is on the up axis. Is the graph linear, proportional or neither?

   • Proportional: every rate is -2, and input 0 gives 0
   • Linear, not proportional: every rate is -2, but no point has input 0
   • Neither: the points go down, not up
6. 5.

   Tala plots five points from a mystery rule. They make a V-like dip. Is the graph linear, proportional or neither?

   • Linear, not proportional: the points are evenly spaced across
   • Neither: the rates are -3, -1, 1 and 3
   • Proportional: the point (0, 0) is on the graph
7. 6.

   Ari fills in x = 0, 1, 2 and 3 for the rule y = x × x + 1. Is it linear, proportional or neither?

   • Linear, not proportional: the rate is 1, and input 0 gives 1
   • Proportional: y grows when x grows
   • Neither: the rates are 1, 3 and 5
8. 7.

   Kira's bath has 30 liters of water in it, and the circle adds 12 liters each minute. Input: minutes. Output: liters. Is it linear, proportional or neither?

   • Proportional: 12 more liters every minute, so the line is straight
   • Linear, not proportional: 12 liters each minute, but it is 30 liters at minute 0
   • Neither: the tub will overflow
9. 8.

   Luz builds solid cubes from toy blocks. Edges of 1, 2 and 3 blocks need 1, 8 and 27 blocks. Input: edge. Output: blocks. Is it linear, proportional or neither?

   • Proportional: an edge of 0 blocks needs 0 blocks, and the count grows
   • Neither: the blocks go up by 7, then 19
   • Linear, not proportional: every cube has 6 faces

10. Use the table

    input: week	output: height in cm
    1	5
    2	8
    3	11
    4	15
    5	17

    Rows sorted by input.

11. 9.

    Milo copied a plant log, and one row has a copying slip. All the other rows are on one line. Which input's row is off the line?

    4
12. 10.

    In math club, Noah finds one wrong row in a table. The other rows are all on one line. Which input's row is off the line?

    6