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# Basic Math/Direct variation

Question
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

Basic Math

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#### Pawan Musale

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I can answer Basic Mathematics questions like: Natural Numbers, Integers, Real Numbers, Complex Numbers, Number Theory, Geometry, Trigonometry, Graph Theory, Square Roots, Basic Integration, Profit-Loss problems, Work-Time problems, Equations etc I can try to answer questions of probability and set theory

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I was 18th in High School Scholarship examination in Maharashtra State of India. I was second in Mathematics in Maharashtra State in Secondary School Certificate examination.