Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 44

Find the intercepts and graph of the line $\frac{1}{3}x - \frac{1}{4}y = 1$.

$x$-intercepts:


$\begin{equation} \begin{aligned} \frac{1}{3}x - \frac{1}{4}y =& 1 && \text{Given equation} \\ \\ \frac{1}{3}x - \frac{1}{4}(0) =& 1 && \text{To find the $x$-intercept, we let $y = 0$ and solve for $x$} \\ \\ \frac{1}{3}x =& 1 && \\ \\ x =& 3 && \end{aligned} \end{equation}$


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

$y$-intercepts:


$\begin{equation} \begin{aligned} \frac{1}{3}x - \frac{1}{4}y =& 1 && \text{Given equation} \\ \\ \frac{1}{3}(0) - \frac{1}{4}y =& 1 && \text{To find the $y$-intercept, we let $x = 0$ and solve for $y$} \\ \\ \frac{-1}{4}y =& 1 && \\ \\ y =& -4 && \end{aligned} \end{equation}$



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

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