Question

If y varies directly with x, and If y = -36 when x = 6, how do you find x when y = 42?

Answer 1

`x=-7`

Explanation:

If y varies directly with x that means:

`y=kx`

where `k` is a constant.

When we say a variable varies directly with another variable, that is another way of saying that if the first variable increases, the second variable increases and vice-versa.

Now, we simple solve for `k` and substitute the values of `x` and `y` to find the constant `k`.

`k=y/x`

`k=(-36)/6`

`k=-6`

To find `x` when `y=42`, we will solve for x in the original equation and substitute the values of `k` and `y`.

`y=kx`

`x=y/k`

`x=42/-6`

`x=-7`