Chapter 3.4, Problem 8CYU

To determine

Write the direct variation equation that relates x and y.

Answer to Problem 8CYU

Therefore, the direct variation equation is $y=-\frac{11}{6}x$ and $x=-24$ when y = 44

Explanation of Solution

Given:

y varies directly as x , and y = − 11 when x = 6.

Concept Used:

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

Calculation:

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

Therefore, the direct variation equation is $y=-\frac{11}{6}x$

Find the value of x when y = 44

  $\begin{array}{l}y=-\frac{11}{6}x\\ 44=-\frac{11}{6}x[y=44]\\ -\frac{6}{11}·44=-\frac{6}{11}·-\frac{11}{6}x\text{[}\text{Multiply}\text{both}\text{sides}\text{by}(-\frac{6}{11})\text{]}\\ x=-24\end{array}$

Thus, therefore, the direct variation equation is $y=-\frac{11}{6}x$ and $x=-24$ when y=44