Question

How do i write a direct variation given that y varies directly with xx: 15 y: -5

Answer 1

When we say that y varies directly with x, we mean that whatever value x is scaled up by, y will be scaled up by, too. The simplest kind of direct variation is one where y = x for all values of x. If you multiply x by some value, y must be multiplied by that same value.

More generally, though, you'll have something of the form y = kx, where the variable k here is referred to as the constant of proportionality. Another way you can think of k is as the ratio of y to x.

In this problem, you're given a set of values for x and y, and you'll need to use those to find the constant of proportionality before you set up an equation relating x to y. Substituting our general equation y = kx for the given values, we have:

-5 = k(15)

To get k, simply divide both sides by 15 to obtain:

k = -5/15 = -1/3

So, our general equation, for any x, would be y = (-1/3)x