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: x	output: y
   1	4
   3	10
   3	11
   5	16
   0	1

2. 1.

   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
3. 2.

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

   • 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
   • 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?

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

   Kira meets the rule y = 3 − x ÷ 2 in math club and fills in x = 0, 2, 4 and 6. Is it linear, proportional or neither?

   • Neither: the rule divides
   • Linear, not proportional: every rate is -1/2, but input 0 gives 3
   • Proportional: every rate is -1/2, so the line is straight
7. 6.

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

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

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

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

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

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