Question

Suppose y varies directly with x. If y = -4 when x = 8, what is the equation of direct variation?

Complete the steps to write the equation of direct variation.
1. Start with the equation of direct variation y = kx.
2. Substitute in the given values for x and y to get
3. Solve fork to get
4. Write the direct variation equation with the value found for k. The equation is​

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 also know that }~~ \begin{cases} y=-4\\ x=8 \end{cases}\implies -4=k(8)\implies \cfrac{-4}{8}=k\implies -\cfrac{1}{2}=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{2}x~\hfill`

Answer 2

k = -1/2

y= -1/2x

Explanation:

y = kx

We know y = -4 and x=8

-4 = k*8

Divide each side by 9

-4/8 = 8k/8

-1/2 =k

y= -1/2x