Question

Write the equation of this line in slope-intercept form.

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

`(\stackrel{x_1}{-40}~,~\stackrel{y_1}{-50})\qquad (\stackrel{x_2}{40}~,~\stackrel{y_2}{-30}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-30}-\stackrel{y1}{(-50)}}}{\underset{\textit{\large run}} {\underset{x_2}{40}-\underset{x_1}{(-40)}}} \implies \cfrac{-30 +50}{40 +40} \implies \cfrac{ 20 }{ 80 } \implies \cfrac{1}{4}`

`\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}{(-50)}=\stackrel{m}{\cfrac{1}{4}}(x-\stackrel{x_1}{(-40)}) \implies y +50 = \cfrac{1}{4} ( x +40) \\\\\\ y-50=\cfrac{1}{4}x+10\implies {\Large \begin{array}{llll} y=\cfrac{1}{4}x+60 \end{array}}`