9th grade Direct variation y = kx and inverse variation xy = k worksheet

Direct variation y = kx and inverse variation xy = k

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
   3	8

   First find k.

2. 1.

   Zee knows y varies inversely with x, and y = 8 when x = 3. What is the rule, in the form y = k/x?
3. 2.

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

4. Input–output table

   hoses	hours
   6	10
   5	?

5. 3.

   Ari's class has 6 hoses filling a pool in 10 hours, all at the same rate. How many hours would 5 hoses need?
6. 4.

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

7. Input–output table with two rows

   The second row has its input doubled or tripled.

8. 5.

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

   • y is halved
   • y doubles
   • y goes up by 2
9. 6.

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

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

    Pia knows y varies inversely with x. If x triples, what happens to y?

    • y goes down by 3
    • y is multiplied by 3
    • y is divided by 3

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?
13. 9.

    Milo knows y varies directly with x, and y = 6 when x = 8. What is y when x = 20?
14. 10.

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