Chapter 5.2, Problem 11P

Suppose y varies directly with $x$.

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

Then find the value of $y$

when $x=8$. $y=1.85$

when $x=0.925$.

To determine

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

Answer to Problem 11P

The equation of variation is $y=2x$ .

Value of y is 16 when $x=8.$

Explanation of Solution

Given information:

  $y=1.85$ when $x=0.925$

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,

  $\begin{array}{l}\frac{y}{x}=\frac{1.85}{0.925}\\ y=2x\end{array}$

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

  $\begin{array}{l}y=2\left(8\right)\\ y=16\end{array}$

Hence the equation of variation is $y=2x$ .

Value of y is 16 when $x=8.$