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?

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

   Noah sorts a mystery table and sees the outputs go up by 4 each row. Is it linear, proportional or neither?

   • Proportional: every output is odd
   • Linear, not proportional: every jump is 4, and input 0 gives 1
   • Neither: the rates are 4, 2 and 4
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
   • Proportional: the point (0, 0) is on the graph
   • Neither: the rates are -3, -1, 1 and 3
7. 6.

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

   • Linear, not proportional: every rate is -3, but input 0 gives 2
   • Proportional: every rate is -3, so the line is straight
   • Neither: the outputs go down
8. 7.

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

   • Proportional: input 0 gives 0, and the outputs grow
   • Neither: the rates are 2, 6 and 10
   • Proportional: the rate is 2, and input 0 gives 0
9. 8.

   Esme's snowman is 150 cm tall at noon. On a sunny afternoon it melts 4 cm each hour. Input: hours after noon. Output: height. Is it linear, proportional or neither?

   • Proportional: it melts 4 cm every hour, so the line is straight and steady
   • Neither: the snowman gets shorter, not taller
   • Linear, not proportional: 4 cm less each hour, but it is 150 cm at hour 0
10. 9.

    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?

    • Neither: the tub will overflow
    • Linear, not proportional: 12 liters each minute, but it is 30 liters at minute 0
    • Proportional: 12 more liters every minute, so the line is straight
11. 10.

    Rows sorted by input. 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