Question

Write the equation of the line that passes through the points (-6,-3) and (2,0). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

`(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-6)}}} \implies \cfrac{0 +3}{2 +6} \implies \cfrac{ 3 }{ 8 }`

`\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}{(-3)}=\stackrel{m}{\cfrac{3}{8}}(x-\stackrel{x_1}{(-6)}) \implies y +3 = \cfrac{3}{8} ( x +6) \\\\\\ y+3=\cfrac{ 3 }{ 8 }x+\cfrac{9}{4}\implies y=\cfrac{ 3 }{ 8 }x+\cfrac{9}{4}-3\implies {\Large \begin{array}{llll} y=\cfrac{ 3 }{ 8 }x-\cfrac{3}{4} \end{array}}`