Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 112

Graph $3x+ y = -5$ by using $x$- and $y$-intercepts

$x$-intercept:


$
\begin{equation}
\begin{aligned}

3x+ y =& -5
&& \text{Given equation}
\\
3x+ 0 =& -5
&& \text{To find the $x$-intercept, let } y = 0
\\
3x =& -5
&& \text{Divide by } 3
\\
x =& \frac{-5}{3}
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $\displaystyle \left( \frac{-5}{3}, 0 \right)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

3x+ y =& -5
&& \text{Given equation}
\\
3(0)+ y =& -5
&& \text{To find the $y$-intercept, let } x=0
\\
y =& -5
&&

\end{aligned}
\end{equation}
$



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

Graph the ordered pairs $\displaystyle \left( \frac{-5}{3}, 0 \right)$ and $(0,-5)$. Draw a straight line through the points.