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?

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

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

   • Proportional: every rate is 1 1/2, and input 0 gives 0
   • Linear, not proportional: every rate is 1 1/2, but no row has input 0
   • Neither: the outputs jump 4 1/2, 1 1/2 and 4 1/2
4. 3.

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

   • Proportional: every output is a whole number
   • Neither: the rates are 2, 2 and 5/2
   • Linear, not proportional: the rate is 2, and input 0 gives 3
5. 4.

   Bo meets the rule y = 3(x + 2) in math club. 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 6
   • Neither: the rule has parentheses, so it does not make a straight line
6. 5.

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

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

   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
   • Proportional: the point (0, 0) is on the graph
   • Neither: the rates are 7, 1, 1 and 7
8. 7.

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

   • Neither: the rate is a fraction
   • Proportional: every rate is 2/3, and input 0 gives 0
   • Linear, not proportional: every rate is 2/3, but no point has input 0
9. 8.

   Tala's science video drops a ball: it falls about 5 m by 1 second, 20 m by 2 seconds and 45 m by 3 seconds. Input: seconds. Output: meters. Is it linear, proportional or neither?

   • Linear, not proportional: the ball falls faster and faster
   • Proportional: at 0 seconds it has fallen 0 m, and the distance grows
   • Neither: the ball falls 5 m, then 15 m, then 25 m more

10. Use the table

    input: x	output: y
    -2	10
    0	6
    1	?
    5	-4

    Rows sorted by input.

11. 9.

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

    4
12. 10.

    Milo's math-club table is linear, but one output is missing. What output goes with input 2?

    6