Question

Write an equation of the line in​ point-slope form that passes through the given points. ​(​5,5​) and ​(​6,9​)

Answer 1

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{5}}} \implies \cfrac{ 4 }{ 1 } \implies 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}{5}=\stackrel{m}{ 4}(x-\stackrel{x_1}{5}) \\\\\\ y-5=4x-20\implies {\Large \begin{array}{llll} y=4x-15 \end{array}}`