Question

Y varies directly as x. If y = 64 when x = 8, find y when x is 10.
Simply the answer

Answer 1

y = 80

Explanation:

When two variables are directly proportional then:

`\boxed{y \propto x \implies y=kx}`

where k is the constant of proportionality.

The constant of proportionality is the constant value of the ratio between two variables.

Therefore, to find the constant of proportionality, divide the y-value by its corresponding x-value. Therefore, if y = 64 when x = 8:

`\begin{aligned}\implies y=kx \implies k&=(y)/(x)\\k&=(64)/(8)\\k&=8\end{aligned}`

Substitute the found value of k back into the formula to create an equation for the given relationship:

`\implies y=8x`

To find y when x is 10, substitute x = 10 into the found equation:

`\implies y=8(10)=80`

Therefore, the value of y when x is 10 is 80.