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
   • Linear, not proportional: every rate is 3, but input 0 gives 1
   • Proportional: input 0 gives 1
3. 2.

   Bo meets the rule y = 3(x + 2) in math club. Is it linear, proportional or neither?

   • Neither: the rule has parentheses, so it does not make a straight line
   • Linear, not proportional: every rate is 3, but input 0 gives 6
   • Proportional: every rate is 3, so the line is straight
4. 3.

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

   • Proportional: the point (0, 0) is on the graph
   • Neither: the rates are 7, 1, 1 and 7
   • Linear, not proportional: the points rise from left to right
5. 4.

   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
   • Linear, not proportional: every rate is 2/3, but no point has input 0
   • Neither: the rate is a fraction
6. 5.

   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
7. 6.

   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
   • Linear, not proportional: the ball falls faster and faster
   • Proportional: at 0 seconds it has fallen 0 m, and the distance grows
8. 7.

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

9. Use the table

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

   Rows sorted by input.

10. 8.

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

    14
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