A line goes through the points (-3, 5) and (2, -4). Write the equation of the line in slope-intercept form. Show your work for full credit. Anything you do "in your head&qu…

Question

A line goes through the points (-3, 5) and (2, -4). Write the equation of the line in slope-intercept

form. Show your work for full credit. Anything you do "in your head" or on a calculator needs to be
written down here using numbers/operations/variables.. (How did you go from those two points
to having the equation in slope-intercept form?) Do not draw graphs to answer this question,
you must complete this problem algebraically (Using numbers, variables, and/or symbols).
Circle or highlight your answer.

Answer 1

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-3)}}} \implies \cfrac{-9}{2 +3} \implies -\cfrac{ 9 }{ 5 }`

`\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{ 9 }{ 5 }}(x-\stackrel{x_1}{(-3)}) \implies y -5= -\cfrac{ 9 }{ 5 } (x +3) \\\\\\ y-5=-\cfrac{ 9 }{ 5 }x-\cfrac{ 27 }{ 5 }\implies y=-\cfrac{ 9 }{ 5 }x-\cfrac{ 27 }{ 5 }+5\implies {\LARGE \begin{array}{llll} y=-\cfrac{ 9 }{ 5 }x-\cfrac{2}{5} \end{array}}`