Direct variation y = kx and inverse variation xy = k

Answer Key - Grade 9 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. Read this first

   Input–output table

   x	y
   4	12

   First find k.

2. 1.

   Zee knows y varies directly with x, and y = 12 when x = 4. What is the rule, in the form y = kx?

   y = 3x
3. 2.

   Ren knows y varies directly with x, and y = 20 when x = 5. What is the rule, in the form y = kx?

   y = 4x
4. 3.

   Esme knows y varies inversely with x, and y = 5 when x = 6. What is the rule, in the form y = k/x?

   y = 30/x

5. Input–output table

   painters	hours
   4	6
   3	?

6. 4.

   Noah and 3 friends paint a fence together. The 4 painters finish in 6 hours at the same pace. How many hours would 3 painters need?

   8
7. 5.

   Luz's bus trip takes 3 hours at 40 mph. How many hours would the same trip take at 60 mph?

   2

8. Input–output table with two rows

   The second row has its input doubled or tripled.

9. 6.

   Tala knows y varies directly with x. If x doubles, what happens to y?

   • y doubles
   • y is halved
   • y goes up by 2
10. 7.

    Jun knows y varies inversely with x. If x doubles, what happens to y?

    • y is halved
    • y goes down by 2
    • y doubles

11. Input–output table

    x	y
    6	4
    15	?

    The constant k is not a whole number.

12. 8.

    Bo knows y varies directly with x, and y = 4 when x = 6. What is y when x = 15?

    10
13. 9.

    Milo knows y varies directly with x, and y = 6 when x = 8. What is y when x = 20?

    15
14. 10.

    Zee knows y varies directly with x, and y = 6 when x = 9. What is y when x = 21?

    14