[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -3}}\quad ,&{{ -1}})\quad
\end{array}
\\\quad \\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{2}{5}
\\ \quad \\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}[/tex]
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-1)=\cfrac{2}{5}(x-(-3))
\\\\\\
y+1=\cfrac{2}{5}(x+3)\implies y+1=\cfrac{2}{5}x+\cfrac{6}{5}\implies y=\cfrac{2}{5}x+\cfrac{6}{5}-1
\\\\\\
\begin{array}{llll}
y=&\cfrac{2}{5}x&+\cfrac{1}{5}\\
&\uparrow &\quad \uparrow \\
&slope&y-intercept
\end{array}\impliedby \textit{slope-intercept form}[/tex]
