For the equation 4y=8x, what is the constant of variation?

1 Answer
Jan 9, 2017

The constant of variation is 2.

Explanation:

We can solve this equation for y in terms of x, by dividing both sides by 4:

4y=8x

4y=8x4

4y=2x

Now we have an equation that says, "y is always 2 times as much as x is". It is this 2 that is our constant of variation, because every time x goes up by 1, y will go "up" by 2 (i.e. down by 2).

Can we show this?

Let x=x+1 (i.e. x is one more than x). If y is in direct variation with x, with a constant of variation of 2, then

y=2x

Which means

y=2(x+1) (since x=x+1)
y=2x2

But wait, y=2x, so we have

y=y2

And there we go! When x is 1 more than x, we see y is 2 less than y. In other words: when x goes up by 1, y goes down by 2.