Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 102

Graph $2x-3y = -6$ by using $x$- and $y$-intercepts

$x$-intercept:


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


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

$y$-intercept:


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



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

Graph the ordered pairs $(-3,0)$ and $(0,2)$. Draw a straight line through the points.