Question

Write the slope-intercept form of the equation of the line that passes through the given points: (-4, -2) and (3, -1)

Answer 1

$\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-4)}}}\implies \cfrac{-1+2}{3+4}\implies \cfrac{1}{7}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{\cfrac{1}{7}}[x-\stackrel{x_1}{(-4)}]\implies y+2=\cfrac{1}{7}(x+4) \\\\\\ y+2=\cfrac{1}{7}x+\cfrac{4}{7}\implies y=\cfrac{1}{7}x+\cfrac{4}{7}-2\implies y=\cfrac{1}{7}x-\cfrac{10}{7}$