Question

A line with a slope of 7 passes through the points (-7, 5) and (g, -2). What is the value of g?

g=

Answer 1

`(\stackrel{x_1}{-7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{g}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{g}-\underset{x_1}{(-7)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 7 }\implies \cfrac{-7}{g+7}=7\implies -7=7(g+7) \\\\\\ \cfrac{-7}{7}=g+7\implies -1=g+7\implies \boxed{-8=g}`