Beginning Algebra With Applications, Chapter 5, Review Exercises, Section Review Exercises, Problem 10

Determine the $x$- and $y$-intercepts for $6x-4y=12$.

$x$-intercepts:


$
\begin{equation}
\begin{aligned}

6x-4y =& 12
&& \text{Given equation}
\\
6x-4(0) =& 12
&& \text{To find the $x$-intercept, let } y=0
\\
6x =& 12
&& \text{Simplify}
\\
x =& 2
&& \text{Divide by } 6

\end{aligned}
\end{equation}
$


The $x$-intercept is $(2,0)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

6x-4y =& 12
&& \text{Given equation}
\\
6(0)-4y =& 12
&& \text{To find the $y$-intercept, let } x=0
\\
-4y =& 12
&& \text{Simplify}
\\
y =& -3
&& \text{Divide by } -4

\end{aligned}
\end{equation}
$


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