Chapter 5.2, Problem 12P

Suppose $y$ varies directly with $x$.

Write a direct variation equation that relates $x$ and $y$.

Then find the value of $y$

when $x=8$. $y=1\frac{2}{9}$

when $x=3\frac{2}{3}$.

To determine

To write a direct variation equation and then to find value of y when $x=8.$

Answer to Problem 12P

The equation of variation is $y=\frac{1}{3}x$ .

Value of y is $\frac{8}{3}$ when $x=8.$

Explanation of Solution

Given information:

  $y=1\frac{2}{9}$ when $x=3\frac{2}{3}.$

Direct variation means when the given variables always have the same ratio. That is $\frac{y}{x}=k$ , where k is any constant.

Hence we can write given condition as,

  $\begin{array}{l}\frac{y}{x}=\frac{1\frac{2}{9}}{3\frac{2}{3}}=\frac{\left(\frac{11}{9}\right)}{\left(\frac{11}{3}\right)}\\ y=\frac{1}{3}x\end{array}$

Now we shall put $x=8.$ we get,

  $\begin{array}{l}y=\frac{1}{3}\left(8\right)\\ y=\frac{8}{3}\end{array}$

Hence the equation of variation is $y=\frac{1}{3}x$ .

Value of y is $\frac{8}{3}$ when $x=8.$