Question

Write an equation of the line in​ point-slope form that passes through the given points in the table. Then write the equation in​ slope-intercept form.

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

`(\stackrel{x_1}{-16}~,~\stackrel{y_1}{-69})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-33}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-33}-\stackrel{y1}{(-69)}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{(-16)}}} \implies \cfrac{-33 +69}{8 +16} \implies \cfrac{ 36 }{ 24 } \implies \cfrac{ 3 }{ 2 }`

`\begin{array}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}{(-69)}=\stackrel{m}{ \cfrac{ 3 }{ 2 }}(x-\stackrel{x_1}{(-16)}) \\\\\\ y +69 = \cfrac{ 3 }{ 2 } ( x +16)\implies y+69=\cfrac{ 3 }{ 2 }x+24\implies {\Large \begin{array}{llll} y=\cfrac{ 3 }{ 2 }x-45 \end{array}}`