Chapter 5.2, Problem 9P

Suppose $y$ varies directly with $x$.

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

Then find the value of $y$

when $x=8$. $y=2$

when $x=5$.

To determine

To find: The direct variation equation that relates $x$ and $y$ if $y=2$ when $x=5$ , then find the value of $y$ when $x=8$ .

Answer to Problem 9P

The equation of the direct variation is $y=\frac{2}{5}x$ and the value of $y$ when $x=8$ is $\frac{16}{5}$ .

Explanation of Solution

Given information:

  $y=2$ when $x=5$

Given that $y$ varies directly with $x$ and $y=2$ when $x=5$ .

Thus, we have

  $\begin{array}{l}y=kx\\ \Rightarrow 2=k(5)=5k\\ \Rightarrow k=\frac{2}{5}\end{array}$

So the constant of variation equation is $y=\frac{2}{5}x$ .

To find the value of $y$ when $x=8$ .

  $y=\frac{2}{5}(8)=\frac{16}{5}$

Conclusion:

Therefore, the equation of the direct variation is $y=\frac{2}{5}x$ and the value of $y$ when $x=8$ is $\frac{16}{5}$ .