a)
[tex]\bf y=mx+b\implies y=\stackrel{slope}{3}x\stackrel{y-intercept}{-2}\implies y=3x-2[/tex]
b)
[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 2}}\quad ,&{{ 5}})\quad
% (c,d)
&({{ -4}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-5}{-4-2}\implies \cfrac{-4}{-6}\implies \cfrac{2}{3}[/tex]
[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-5=\cfrac{2}{3}(x-2)\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-5=\cfrac{2}{3}x-\cfrac{4}{3}\implies y=\cfrac{2}{3}x-\cfrac{4}{3}+5\implies y=\cfrac{2}{3}x+\cfrac{11}{3}[/tex]
