Question

If y varies directly as x, and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this relation?

Answer 1

The numeric constant of variation in this relation will be +10 or -10.

Explanation

$y$ varies directly as $x$ means : $y= k*x$ , where k is the proportional constant.

Given that, $y=400$ when $x=r$ . So....

$400=k*r ..............................(1)$

and $y=r$ when $x=4$. So.....

$r=k*4\\ \\ r=4k ................................(2)$

Now substituting this $r=4k$ into equation (1), we will get.....

$400=k*4k\\ \\ 400=4k^2\\ \\ k^2= 100\\ \\ k= +/-\sqrt{100}=+/- 10$

So, the numeric constant of variation in this relation will be +10 or -10.