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 $(0,-4)$.