Question

What is the equation of the line that passes through (7,4) and (4, -2)?

Oy=2x-10
Oy=-2x-10
Oy=2x+18
Oy=-2x+18

Answer 1

`(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{7}}} \implies \cfrac{ -6 }{ -3 }\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}{4}=\stackrel{m}{2}(x-\stackrel{x_1}{7}) \\\\\\ y-4=2x-14\implies {\Large \begin{array}{llll} y=2x-10 \end{array}}`