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 .