Question

A line includes the points (7, 15) and (-14, 9). 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}{7}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{-14}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{15}}}{\underset{run} {\underset{x_2}{-14}-\underset{x_1}{7}}} \implies \cfrac{ -6 }{ -21 } \implies \cfrac{2 }{ 7 }`

`\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}{15}=\stackrel{m}{ \cfrac{2 }{ 7 }}(x-\stackrel{x_1}{7}) \\\\\\ y-15=\cfrac{2 }{ 7 }x-2\implies {\Large \begin{array}{llll} y=\cfrac{2 }{ 7 }x+13 \end{array}}`