Precalculus, Chapter 1, 1.3, Section 1.3, Problem 92

a. Determine the intercepts of the graph of the equation $3x - 2y = 6$.

$x$-intercepts:


$
\begin{equation}
\begin{aligned}

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

\end{aligned}
\end{equation}
$


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


$y$-intercepts:


$
\begin{equation}
\begin{aligned}

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

\end{aligned}
\end{equation}
$


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


Graph the equation