Question

The graph of a proportional relationship contains the point (8, 4).

What is the corresponding equation?

Enter your answer as a fraction in simplest form

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}\\\\ -------------------------------\\\\ (\stackrel{x}{8}~~,~~\stackrel{y}{4})\implies \begin{cases} x=8\\ y=4 \end{cases}\implies 4=k8\implies \cfrac{4}{8}=k\implies \cfrac{1}{2}=k \\\\\\ \boxed{y=\cfrac{1}{2}x}`