Intermediate Algebra, Chapter 3, 3.3, Section 3.3, Problem 42

Determine an equation of the line that satisfies the condition "$x$-intercept $(-2,0)$; slope $-5$".

(a) Write the equation in standard form.

Use the Point Slope Form of the equation of a line with $(x_1,y_1) = (-2,0)$ and $m = -5$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
&& \text{Point Slope Form}
\\
\\
y - 0 =& -5 [x - (-2)]
&& \text{Substitute $x = -2, y = 0$ and } m = -5
\\
\\
y =& -5x - 10
&& \text{Distributive Property}
\\
\\
5x + y =& -10
&& \text{Standard Form}

\end{aligned}
\end{equation}
$



(b) Write the equation in slope-intercept form.


$
\begin{equation}
\begin{aligned}

5x + y =& -10
&& \text{Standard Form}
\\
y =& -5x - 10
&& \text{Slope Intercept Form}

\end{aligned}
\end{equation}
$