Question

What is an equation of the line that passes through the points (6, 5)(6,5) and (7, 7)(7,7)?.

Answer 1

`(\stackrel{x_1}{6}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{6}}} \implies \cfrac{ 2 }{ 1 } \implies 2`

`\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}{ 2}(x-\stackrel{x_1}{6}) \\\\\\ y-5=2x-12\implies {\Large \begin{array}{llll} y=2x-7 \end{array}}`