Question

A line includes the points (0, –16) and (18, –15). What is its equation in slope-intercept form?

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

Answer 1

`(\stackrel{x_1}{0}~,~\stackrel{y_1}{-16})\qquad (\stackrel{x_2}{18}~,~\stackrel{y_2}{-15}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-15}-\stackrel{y1}{(-16)}}}{\underset{run} {\underset{x_2}{18}-\underset{x_1}{0}}} \implies \cfrac{-15 +16}{18} \implies \cfrac{ 1 }{ 18 } \implies \cfrac{1 }{ 18 }`

`\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}{(-16)}=\stackrel{m}{ \cfrac{1 }{ 18 }}(x-\stackrel{x_1}{0}) \implies y +16 = \cfrac{1 }{ 18 } ( x -0) \\\\\\ y+16=\cfrac{1 }{ 18 }x\implies {\Large \begin{array}{llll} y=\cfrac{1 }{ 18 }x-16 \end{array}}`