Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 116

Graph $3x-2y=-6$ using a graphing device. Verify that the graph has the correct $x-$ and $y$-intercepts.







$x$-intercept:


$\begin{equation} \begin{aligned} 3x-2y=& -6 && \text{Given equation} \\ 3x-2(0) =& -6 && \text{To find the $x$-intercept, let } y = 0 \\ 3x =& -6 && \text{Divide by } 3 \\ x =& -2 && \end{aligned} \end{equation}$


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

$y$-intercept:


$\begin{equation} \begin{aligned} 3x-2y=& -6 && \text{Given equation} \\ 3(0)-2y=& -6 && \text{To find the $y$-intercept, let } x=0 \\ -2y =& -6 && \text{Divide by } -2 \\ y =& 3 && \end{aligned} \end{equation}$



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