Linear, proportional or neither?

Grade 8 Math Worksheet - Challenge Me

Circle the best answer.

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.

   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
   • Neither: input 3 has two different outputs
   • Proportional: 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?

   • Neither: the outputs jump 4 1/2, 1 1/2 and 4 1/2
   • 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
5. 4.

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

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

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

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

   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
   • Linear, not proportional: every rate is -1/2, but input 0 gives 1
   • Proportional: every rate is -1/2, so the line is straight
8. 7.

   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
9. 8.

   Ren lights a 30 cm candle. It burns down 1.5 cm each hour. Input: hours. Output: height. Is it linear, proportional or neither?

   • Proportional: it burns 1.5 cm every hour, so the line is straight and steady
   • Neither: 1.5 is not a whole number
   • Linear, not proportional: 1.5 cm less each hour, but it is 30 cm at hour 0
10. 9.

    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?

    • 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
    • Neither: the bottle will be empty after 6 hours

11. Use the table

    input: x	output: y
    2	1
    4	5
    6	9
    4	6
    0	-3

12. 10.

    Bo's table has two rows for input 4, from two tries at the same puzzle. Is it linear, proportional or neither?

    • Proportional: every rate is 2
    • Neither: input 4 has two different outputs
    • Linear, not proportional: every rate is 2, but input 0 gives -3