Intermediate Algebra, Chapter 3, Summary Exercises, Section Summary Exercises, Problem 12

Write an equation of the line "through $(4,-2)$ with slope $-3$".

(a) In slope-intercept form

Using Point Slope Form


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&& \text{Point Slope Form}
\\
y - (-2) =& -3(x - 4)
&& \text{Substitute } x = 4, y = -2 \text{ and } m = -3
\\
y + 2 =& -3x + 12
&& \text{Distributive Property}
\\
y =& -3x + 12 -2
&& \text{Subtract each side by $2$}
\\
y =& -3x + 10
&& \text{Slope Intercept Form}

\end{aligned}
\end{equation}
$



(b) In standard form


$
\begin{equation}
\begin{aligned}

y =& -3x + 10
&& \text{Slope Intercept Form}
\\
3x + y =& 10
&& \text{Standard Form}

\end{aligned}
\end{equation}
$