Linear, proportional or neither?

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. Read this first

   Use the table

   input: minutes	output: cups of water
   0.5	3
   2	6
   2.5	7
   5	12

2. 1.

   Ren fills a measuring jug that already had some water in it, and reads it at a few times. Is the table linear, proportional or neither?

   • Linear, not proportional: every rate is 2, but input 0 gives 2
   • Proportional: every rate is 2, so the line is straight
   • Neither: the outputs jump 3, 1 and 5
3. 2.

   In math club, Tala gets a table where two rows were written for input 3. Is it linear, proportional or neither?

   • Linear, not proportional: every rate is 3, but input 0 gives 1
   • Proportional: input 0 gives 1
   • Neither: input 3 has two different outputs
4. 3.

   Zee writes how many cups of flour go into different numbers of cookie batches. Is the table linear, proportional or neither?

   • Neither: the outputs jump 4 1/2, 1 1/2 and 4 1/2
   • Linear, not proportional: every rate is 1 1/2, but no row has input 0
   • Proportional: every rate is 1 1/2, and input 0 gives 0
5. 4.

   Ari's math-club table looks steady at first glance. Is it linear, proportional or neither?

   • Proportional: every output is a whole number
   • Linear, not proportional: the rate is 2, and input 0 gives 3
   • Neither: the rates are 2, 2 and 5/2
6. 5.

   Esme meets the rule y − 4 = 5x in math club. Is it linear, proportional or neither?

   • Neither: y is not by itself
   • Linear, not proportional: every rate is 5, but input 0 gives 4
   • Proportional: every rate is 5, so the line is straight
7. 6.

   Milo plots four points from a rule card. None is on the up axis. Is the graph linear, proportional or neither?

   • Linear, not proportional: every rate is -1/2, but input 0 gives 1
   • Proportional: every rate is -1/2, so the line is straight
   • Neither: the line crosses the x-axis
8. 7.

   Noah plots five points from the rule y = x × x × x. Is the graph linear, proportional or neither?

   • Linear, not proportional: the points rise from left to right
   • Neither: the rates are 7, 1, 1 and 7
   • Proportional: the point (0, 0) is on the graph
9. 8.

   Pia plots four points, skipping x = 0. Is the graph linear, proportional or neither?

   • Linear, not proportional: every rate is 2/3, but no point has input 0
   • Proportional: every rate is 2/3, and input 0 gives 0
   • Neither: the rate is a fraction

10. Use the table

    input: x	output: y
    1	5
    3	11
    4	?
    7	23

    Rows sorted by input.

11. 9.

    Kira's math-club table is linear, but one output is missing. What output goes with input 4?

    14
12. 10.

    Luz's math-club table is linear, but one output is missing. What output goes with input 1?

    4