Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 118

Graph $3x-4y = 4$ using a graphing device. Verify that the graph has the correct $x-$ and $y$-intercepts.







$x$-intercept:


$
\begin{equation}
\begin{aligned}

3x-4y =& 4
&& \text{Given equation}
\\
3x-4(0) =& 4
&& \text{To find the $x$-intercept, let } y = 0
\\
3x =& 4
&& \text{Divide by } 3
\\
x =& \frac{4}{3}
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $\displaystyle \left( \frac{4}{3},0 \right)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

3x-4y =& 4
&& \text{Given equation}
\\
3(0)-4y =& 4
&& \text{To find the $y$-intercept, let } x=0
\\
-4y =& 4
&& \text{Divide by } -4
\\
y =& -1
&&

\end{aligned}
\end{equation}
$



The $y$-intercept is $(0,-1)$