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.

   Zee knows y varies inversely with x, and y = 8 when x = 3. What is the rule, in the form y = k/x?

   y = 24/x
4. 3.

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

   y = 4x
5. 4.

   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

6. Input–output table

   painters	hours
   4	6
   3	?

7. 5.

   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
8. 6.

   Ari's class has 6 hoses filling a pool in 10 hours, all at the same rate. How many hours would 5 hoses need?

   12
9. 7.

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

   2
10. 8.

    The second row has its input doubled or tripled. Tala knows y varies directly with x. If x doubles, what happens to y?

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

11. Input–output table

    x	y
    8	6
    20	?

    The constant k is not a whole number.

12. 9.

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

    15
13. 10.

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

    14