Precalculus, Chapter 1, 1.2, Section 1.2, Problem 26

Determine the intercepts and graph equation $5x + 2y = 10$ by plotting points. Be sure to label the intercepts.

$x$-intercept:


$\begin{equation} \begin{aligned} 5x + 2y =& 10 && \text{Given equation} \\ 5x + 2(0) =& 10 && \text{To find the $x$-intercept, we let } y = 0 \\ 5x =& 10 && \\ x =& 2 && \end{aligned} \end{equation}$


The $x$-intercept is $(2,0)$

$y$-intercept:


$\begin{equation} \begin{aligned} 5x + 2y =& 10 && \text{Given equation} \\ 5(0) + 2y =& 10 && \text{To find the $y$-intercept, we let } x = 0 \\ 2y =& 10 && \\ y =& 5 && \end{aligned} \end{equation}$


The $y$-intercept is $(0,5)$