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?

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

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

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

   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
   • 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
5. 4.

   Jun meets the rule y = x(x + 4) in math club. Is it linear, proportional or neither?

   • Proportional: input 0 gives 0, and the outputs grow
   • Neither: the rates are 5, 7 and 9
   • Proportional: the rate is 5, and input 0 gives 0
6. 5.

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

   • Neither: the line crosses the x-axis
   • Proportional: every rate is -1/2, so the line is straight
   • Linear, not proportional: every rate is -1/2, but input 0 gives 1
7. 6.

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

   • Proportional: every rate is 2/3, and input 0 gives 0
   • Neither: the rate is a fraction
   • Linear, not proportional: every rate is 2/3, but no point has input 0
8. 7.

   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?

   • Neither: the ball falls 5 m, then 15 m, then 25 m more
   • Proportional: at 0 seconds it has fallen 0 m, and the distance grows
   • Linear, not proportional: the ball falls faster and faster
9. 8.

   Zee's full water bottle holds 750 mL. On a hike, Zee drinks 125 mL each hour. Input: hours. Output: mL left. Is it linear, proportional or neither?

   • Neither: the bottle will be empty after 6 hours
   • Proportional: 125 mL gone every hour, so the line is straight
   • Linear, not proportional: 125 mL less each hour, but it is 750 mL at hour 0

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.

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

    6