Question

Write a linear equation in

slope-intercept form that passes
through the points (-11,-5) and
(1,2).

Answer 1

`\bf (\stackrel{x_1}{-11}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-11)}}}\implies \cfrac{2+5}{1+11}\implies \cfrac{7}{12}`

`\bf \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}{\cfrac{7}{12}}[x-\stackrel{x_1}{(-11)}]\implies y+5=\cfrac{7}{12}(x+11) \\\\\\ y+5=\cfrac{7}{12}x+\cfrac{77}{12}\implies y=\cfrac{7}{12}x+\cfrac{77}{12}-5\implies y = \cfrac{7}{12}x +\cfrac{17}{12}`