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