[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -3 &,& -3~)
% (c,d)
&&(~ 6 &,& 21~)
\end{array}
\\\\\\
% slope = m
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{21-(-3)}{6-(-3)}\implies \cfrac{21+3}{6+3}[/tex]
[tex]\bf \cfrac{24}{9}\implies \cfrac{8}{3}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-3)=\cfrac{8}{3}[x-(-3)]
\\\\\\
y+3=\cfrac{8}{3}(x+3)\implies y+3=\cfrac{8}{3}x+8\implies y=\cfrac{8}{3}x+5[/tex]
