Precalculus, Chapter 1, 1.3, Section 1.3, Problem 96

a. Determine the intercepts of the graph of the equation $5x + 3y = 18$.

$x$-intercepts:


$
\begin{equation}
\begin{aligned}

5x + 3y =& 18
&& \text{Given equation}
\\
5x + 3(0) =& 18
&& \text{To find the $x$-intercept, we let $y = 0$ and solve for $x$}
\\
5x =& 18
&&
\\
x =& \frac{18}{5}
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $\displaystyle \left( \frac{18}{5},0 \right)$


$y$-intercepts:


$
\begin{equation}
\begin{aligned}

5x + 3y =& 18
&& \text{Given equation}
\\
5(0) + 3y =& 18
&& \text{To find the $y$-intercept, we let $x = 0$ and solve for $y$}
\\
3y =& 18
&&
\\
y =& 6
&&

\end{aligned}
\end{equation}
$


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


Graph the equation