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Is x=2y-12 a direct variation?

Dylan,

The statement " y varies directly as x ," means that when x increases, y increases by the same factor. In other words, y and x always have the same ratio: y/x= k

where k is the constant of variation.

We can also express the relationship between x and y as: y = kx

Now, in your case, x = 2y-12. This expression has -12 as a contstant. This will not keep ratio between y and x (y/x) constant. We will prove this with an example.

(1) Assume y=1. Putting this in equation x=2y-12, we get

x=2*1-12 = 2-12 = -10

Ratio, k = y/x = 1/-10 = -0.1

(2)Assume y=2. Putting this in equation x=2y-12, we get

x=2*2-12 = 4-12 = -8

Ratio, k = y/x = 2/-8 = -0.25

In both of the cases, k is different and hence this is not direct variation.

I hope that this is clear.

All the best!

Regards,

Pawan

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