Question

If y varies directly as x, and y = 2 when x = 4, find y when x = 32.

Answer 1

`\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}`

`\bf \textit{we also know that } \begin{cases} y=2\\ x=4 \end{cases}\implies 2=k(4)\implies \cfrac{2}{4}=k\implies \cfrac{1}{2}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{1}{2}x} \\\\\\ \textit{when x = 32, what's \underline{y}?}\qquad y=\cfrac{1}{2}(32)\implies y=16`

Answer 2

Explanation:

y~x

y=kx

where

y=2,x=4

2=k*4

k=2/4

k=0.5//

find y when x =32

then

y=32*0.5

y=16//