Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 40

Determine the slope and $y$-intercept of the line $\displaystyle \frac{-3}{4}x + \frac{1}{2}y = 0$. Graph the line, labeling any intercepts.

We write the equation $\displaystyle \frac{-3}{4}x + \frac{1}{2}y = 0$ in slope intercept form to find the slope. We get


$\begin{equation} \begin{aligned} \frac{-3}{4}x + \frac{1}{2}y =& 0 && \text{Given equation} \\ \\ \frac{1}{2}y =& \frac{3}{4}x && \text{Add } \frac{3}{4}x \\ \\ y =& \frac{3}{2}x && \text{Multiply both sides by } 2 \end{aligned} \end{equation}$



The slope is $\displaystyle \frac{3}{2}$. To find the $y$-intercept, we let $x = 0$ and solve for $y$. So we have


$\begin{equation} \begin{aligned} y =& \frac{3}{2} (0) \qquad x = 0 \\ y =& 0 \end{aligned} \end{equation}$


The $y$-intercept is .