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 $(0,-1)$