Chapter 9.5, Problem 9PPS

To determine

To find the value of $x_2$ .

Answer to Problem 9PPS

the value of $x_2$ is $-56$

Explanation of Solution

Given information:

x varies directly as y

the value of $x_1=14\text{ when }{y}_1=-2$

Calculation:

The values of $x_2$ can be obtained as

Use a proportion that relates the value

  $\begin{array}{l}\frac{x_1}{y_1}\text{=}\frac{x_2}{y_2}\left[\text{since,direct variation}\right]\\ \end{array}$

Put the values of $x_1=14$ , $y_1=-2$ , $y_2=8$ in above equation

  $\begin{array}{l}\frac{14}{-2}=\frac{x_2}{8}\\ \left(14\right)\left(8\right)=\left(-2\right)\left(x_2\right)\left[\text{cross multiply}\right]\\ 112=-2x_2\left[\text{simplify}\right]\\ x_2=-56\text{ [divide each side by 2] }\end{array}$

Hence,

the value of $x_2$ is $-56$