Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 42

Find the intercepts and graph of the line $x - 2y = 8$.

$x$-intercepts:


$
\begin{equation}
\begin{aligned}

3x + 4y =& 12
&& \text{Given equation}
\\
3x + 4(0) =& 12
&& \text{To find the $x$-intercept, we let $y = 0$ and solve for $x$}
\\
3x =& 12
&&
\\
x =& 4
&&

\end{aligned}
\end{equation}
$


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

$y$-intercepts:


$
\begin{equation}
\begin{aligned}

3x + 4y =& 12
&& \text{Given equation}
\\
3(0) + 4y =& 12
&& \text{To find the $y$-intercept, we let $x = 0$ and solve for $y$}
\\
4y =& 12 && \\
y =& 3 && \\
\end{aligned}
\end{equation}
$



The $y$-intercept is $(0,3)$.

The intercepts are $(4,0)$ and $(0,3)$.