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 $(0,5)$