Question

Write a linear equation in slope -intercept form that passes through the points (-8,4) (1,-5)

Answer 1

`\bf (\stackrel{x_1}{-8}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-8)}}}\implies \cfrac{-9}{1+8}\implies \cfrac{-9}{9}\implies -1`

`\bf \begin{array}c \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}{4}=\stackrel{m}{-1}[x-\stackrel{x_1}{(-8)}]\implies y-4=-(x+8) \\\\\\ y-4=-x-8\implies y=-x-4`