Question

What is the equation of the line that passes through the point (3, -7) and has a slope of

−4/3?

Answer 1

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{3} \\\\\\ \begin{array}ll \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \implies y +7= -\cfrac{4}{3} (x -3) \\\\\\ y+7=-\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x-3 \end{array}}`