[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -3}}\quad ,&{{ 2}})\quad
% (c,d)
&({{ 1}}\quad ,&{{ 5}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{5-2}{1-(-3)}\implies \cfrac{5-2}{1+3}[/tex]
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=\cfrac{3}{4}(x-(-3))\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-2=\cfrac{3}{4}(x+3)\implies y-2=\cfrac{3}{4}x+\cfrac{9}{4}\implies y=\cfrac{3}{4}x+\cfrac{9}{4}+2
\\\\\\
y=\cfrac{3}{4}x+\cfrac{17}{4}[/tex]
