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
   • Linear, not proportional: every rate is -2, but input 0 gives 20
   • Proportional: every rate is -2, so the line is straight
3. 2.

   In math club, Luz gets a table with the rows mixed up. Is it 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 -7
   • Neither: the outputs jump 3, 6 and 6
4. 3.

   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
5. 4.

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

   • Proportional: every rate is -3, so the line is straight
   • Neither: the outputs go down
   • Linear, not proportional: every rate is -3, but input 0 gives 2
6. 5.

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

   • Proportional: y grows when x grows
   • Linear, not proportional: the rate is 1, and input 0 gives 1
   • Neither: the rates are 1, 3 and 5
7. 6.

   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
   • Proportional: the rate is 2, and input 0 gives 0
   • Neither: the rates are 2, 6 and 10
8. 7.

   In Jun's puzzle game, level 1 gives 3 stars, level 2 gives 6, level 3 gives 12 and level 4 gives 24. Input: level. Output: stars. Is it linear, proportional or neither?

   • Linear, not proportional: the stars always go up
   • Neither: the stars go up by 3, then 6, then 12
   • Proportional: 3 more stars a level, and level 0 gives 0
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: x	output: y
    0	-4
    2	0
    4	4
    6	9
    8	12

    Rows sorted by input.

11. 9.

    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
12. 10.

    Pia checks a rule table that should be linear. One row is wrong. Which input's row is off the line?

    2