Direct Variation

by Brooke
(Simpsoville, SC, USA)

Will you explain what direct variation is and give some examples please. This would be greatly appreciated!!

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Karin from Algebra Class Says:



Hi Brooke,

Direct variation can be very confusing for many students, so I will explain it the best I can.

We will use the variables x and y. If I say that y varies directly with x, it means that y is directly proportional to x.

y varies directly to x in algebra means y = Kx (where K is any nonzero constant). This is a linear variation.

So if x increases, y is going to increase proportionately.

The following is what I mean by proportionally:
y = Kx
6 = 3(2)
9 = 3(3)
12 = 3(4)

You may have a direct variation such that
y varies directly with the square of x.

That would mean:
y =Kx2 (Where K is any nonzero constant).

12 = 3(2)2
27 = 3(3)2

A problem that you might see in Algebra is:

y varies directly with x. If y is 20 when x is 5, find y when x is 8.

The first sentence tells you the relationship between x and y. "y varies directly with x" so
y = Kx

You know that y = 20 and x =5, so we need to substitute and solve for K which is the constant.

y = Kx
20 = K(5)

20/5 = 5K/5
4 = K

Now we know: y = 4x

So we can substitute 8 for x to answer the question.

y = 4(8)
y = 32.

When x = 8, y = 32.

I hope this helps you to have a better understanding of Direct Variation.

Please let me know if it helped!

Best of luck,
Karin

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