Question

1. Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x= 12.
y = -10 when x = 2

2. Graph the direct variation equation:

y=2x

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf \textit{\underline{y} varies directly with \underline{x}}\implies y=kx \\\\\\ \textit{we also know that } \begin{cases} y=-10\\ x=2 \end{cases}\implies -10=k2\implies \cfrac{-10}{2}=k \\\\\\ -5=k\qquad thus\qquad \boxed{y=-5x}\\\\ -------------------------------\\\\ \textit{what's \underline{y} when \underline{x} is 12?}\qquad y=-5(12)$