Chapter 3.4, Problem 7CYU

To determine

Write the direct variation equation that relates x and y.

Answer to Problem 7CYU

Therefore, the direct variation equation is $y=\frac{5}{4}x$ and $y=40$ when x = 32

Explanation of Solution

Given:

y varies directly as x , and y = 15 when x = 12, find y when x = 32 Concept Used:

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

Calculation:

  $\begin{array}{l}y=kx(\text{Direct}\text{variation}\text{formula})\\ 15=k·12[\text{Replace}y\text{with}15\text{and}x\text{with}12]\\ \frac{15}{12}=\frac{12k}{12}[\text{Divide}\text{each}\text{side}\text{by}12]\\ k=\frac{5}{4}\end{array}$

Therefore, the direct variation equation is $y=\frac{5}{4}x$

Find the value of y when x = 32

  $\begin{array}{l}y=\frac{5}{4}x\\ y=\frac{5}{4}·32[x=32]\\ y=40\end{array}$

Thus, therefore, the direct variation equation is $y=\frac{5}{4}x$ and $y=40$ when x = 32