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Math Practice

Direct Variation Practice Problems

Find the constant of variation k = y ÷ x, then use y = kx. The word problems cover pay, fuel, springs and circles.

  1. 1.

    varies directly with , and when . What is the constant of variation ?

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    .

  2. 2.

    With , find when .

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    .

  3. 3.

    varies directly with , and when . Find when .

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    , so .

  4. 4.

    The direct variation has what constant of variation?

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    It has the form with .

  5. 5.

    A table shows = 2, 4, 6 and = 7, 14, 21. It is a direct variation. What is ?

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    Every ratio is .

  6. 6.

    Pay varies directly with hours. A worker earns $171 for 9 hours. How much for 25 hours, in dollars?

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    , so pay .

  7. 7.

    A car uses 3 gallons to drive 84 miles. At the same rate, how many miles on 10 gallons?

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    miles per gallon, so .

  8. 8.

    A spring stretches 3 cm under a 6-newton load. Stretch varies directly with load. How far does it stretch under 10 newtons, in cm?

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    , so cm.

  9. 9.

    varies directly with the square of , and when . Find when .

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    , so .

  10. 10.

    A direct variation passes through . What is ?

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    .

  11. 11.

    varies directly with , and when . Write the equation: ?

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    , so .

  12. 12.

    Circumference varies directly with diameter. A circle with diameter 10 has circumference 31.4. What is the circumference when the diameter is 25?

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    , so .
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MPhil in Mathematics, Founder of Mathovia
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Direct Variation Practice Problems

These problems follow the direct variation lesson. In every direct variation the ratio stays the same.

The equation

Common mistakes to watch for

  • Adding a constant. Direct variation is with no ””; its graph always passes through the origin.
  • Finding the wrong way round. . Dividing by gives the reciprocal.
  • Calling every line direct variation. is linear but not direct variation, because is not constant.
  • Forgetting powers. ” varies directly with the square of ” means .

Frequently Asked Questions

How do I find the constant of variation?+

Divide any y-value by its matching x-value: k = y ÷ x.

What if y varies with the square of x?+

Use y = kx², so k = y ÷ x².

How do I type my answers?+

Type numbers without units, fractions like 5/3, and expressions like 2x + h. For intervals use parentheses or brackets and oo for infinity, for example (2, oo).

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