Chapter 3.4, Problem 25PPS

To determine

Write the direct variation equation that relates x and y.

Answer to Problem 25PPS

Therefore, the direct variation equation is $y=\frac{11}{4}x$ and $y=-44$ when $x=-16$

Explanation of Solution

Given:

y varies directly as x , and y = 22 when x = 8.

Concept Used:

Direct variation formula is $y=kx$ , where k is the constant of variation.

Calculation:

  $\begin{array}{l}y=kx(\text{Direct}\text{variation}\text{formula})\\ 22=k·8[\text{Replace}y\text{with}22\text{and}x\text{with}8]\\ \frac{22}{8}=\frac{8k}{8}[\text{Divide}\text{each}\text{side}\text{by}6]\\ k=\frac{11}{4}\end{array}$

Therefore, the direct variation equation is $y=\frac{11}{4}x$

Find the value of y when x = − 16

  $\begin{array}{l}y=\frac{11}{4}x\\ y=\frac{11}{4}·-16[x=-16]\\ y=-44\end{array}$

Thus, therefore, the direct variation equation is $y=\frac{11}{4}x$ and $y=-44$ when $x=-16$