Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 98

Determine the $x$ and $y$-intercepts for $\displaystyle y = \frac{2}{3}x - 4$.

$x$-intercept:


$\begin{equation} \begin{aligned} y =& \frac{2}{3}x - 4 && \text{Given equation} \\ 0 =& \frac{2}{3}x - 4 && \text{To find the $x$-intercept, let } y = 0 \\ \frac{-2}{3} x =& -4 && \text{Subtract } \frac{2}{3}x \\ x =& 6 && \text{Multiply both sides by } \frac{-3}{2} \end{aligned} \end{equation}$


The $x$-intercept is $(6,0)$

$y$-intercept:


$\begin{equation} \begin{aligned} y =& \frac{2}{3} x - 4 && \text{Given equation} \\ y =& \frac{2}{3} (0) - 4 && \text{To find the $y$-intercept, let } x=0 \\ y =& -4 && \end{aligned} \end{equation}$



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