Question

Find the equation of the line passing through the points (40,0) and (20,-2). Write your answer in the form

y=mx+b.

Answer 1

`(\stackrel{x_1}{40}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{20}-\underset{x_1}{40}}} \implies \cfrac{ -2 }{ -20 } \implies \cfrac{ 1 }{ 10 }`

`\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}{0}=\stackrel{m}{ \cfrac{ 1 }{ 10 }}(x-\stackrel{x_1}{40})\implies {\Large \begin{array}{llll} y=\cfrac{1}{10}x+4 \end{array}}`