Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 42

Find the intercepts and graph of the line $x - 2y = 8$.

$x$-intercepts:


$\begin{equation} \begin{aligned} 3x + 4y =& 12 && \text{Given equation} \\ 3x + 4(0) =& 12 && \text{To find the $x$-intercept, we let $y = 0$ and solve for $x$} \\ 3x =& 12 && \\ x =& 4 && \end{aligned} \end{equation}$


The $x$-intercept is $(4,0)$.

$y$-intercepts:


$\begin{equation} \begin{aligned} 3x + 4y =& 12 && \text{Given equation} \\ 3(0) + 4y =& 12 && \text{To find the $y$-intercept, we let $x = 0$ and solve for $y$} \\ 4y =& 12 && \\ y =& 3 && \\ \end{aligned} \end{equation}$



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

The intercepts are $(4,0)$ and $(0,3)$.