Direct variation

Question

The values of x and y vary directly and one pair of values are given. Write an equation that relates x and y. Simplify completely. x=0.1 y=0.9

Answer 1

If x and y vary directly, we can say that y is proportional to x. More specifically, we can write an equation like this:

y = kx

where k is a constant which we don't yet know.

However, if we have a pair of values then we can plug those into the equation to get

0.9 = k(0.1)

=> k=9

Hence our required equation is y = 9x

Note: it doesn't matter which way you go. You could also say x is proportional to y, and x = ky. In which case, 0.1 = k(0.9) => k = 1/9 => x = 1/9 y which is equivalent to 9x = y.

Note: These "varies with" can typically be varies directly (as above kx), varies inversely with (k/x) or varies with the square of (kx²) and so on.