Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 98

Determine the $x$ and $y$-intercepts for $\displaystyle y = \frac{2}{3}x - 4$.

$x$-intercept:


$
\begin{equation}
\begin{aligned}

y =& \frac{2}{3}x - 4
&& \text{Given equation}
\\
0 =& \frac{2}{3}x - 4
&& \text{To find the $x$-intercept, let } y = 0
\\
\frac{-2}{3} x =& -4
&& \text{Subtract } \frac{2}{3}x
\\
x =& 6
&& \text{Multiply both sides by } \frac{-3}{2}

\end{aligned}
\end{equation}
$


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

$y$-intercept:


$
\begin{equation}
\begin{aligned}

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

\end{aligned}
\end{equation}
$



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