Question

Write an appropriate direct variation equation if y = 8 when x = 4.

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}\\\\ \textit{we know that } \begin{cases} y=8\\ x=4 \end{cases}\implies 8=k4\implies \cfrac{8}{4}=k\implies 2=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=2x~\hfill`

Answer 2

For this case we have that by definition, a direct variation is represented as:

`y = kx`

Where:

k: It is the constant of proportionality

So:

`k = \frac {y} {x}`

Substituting the values we have:

`k = \frac {8} {4}`

Finally, the proportionality constant is:

`k = 2`

Answer:

`y=2x`