Precalculus, Chapter 1, 1.3, Section 1.3, Problem 98

a. Determine the intercepts of the graph of the equation $\displaystyle x - \frac{2}{3}y = 4$.

$x$-intercepts:


$
\begin{equation}
\begin{aligned}

x - \frac{2}{3}y =& 4
&& \text{Given equation}
\\
x - \frac{2}{3}(0) =& 4
&& \text{To find the $x$-intercept, we let $y = 0$ and solve for $x$}
\\
x =& 4
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $(4,0)$


$y$-intercepts:


$
\begin{equation}
\begin{aligned}

x - \frac{2}{3}y =& 4
&& \text{Given equation}
\\
0 - \frac{2}{3}y =& 4
&& \text{To find the $y$-intercept, we let $x = 0$ and solve for $y$}
\\
- \frac{2}{3}y =& 4
&&
\\
y =& -6
&&

\end{aligned}
\end{equation}
$


The $y$-intercept is $(0,-6)$


Graph the equation