Question

Find the slope intercept form

x- 1,2,3,4
y- -3,-8, -13, -18

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}{2}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-18}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-18}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ -18 +8 }{ 2 } \implies \cfrac{ -10 }{ 2 } \implies -5`

`\begin{array} \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}{(-8)}=\stackrel{m}{-5}(x-\stackrel{x_1}{2}) \implies y +8 = -5 ( x -2) \\\\\\ y +8 = -5 x +10 \implies {\Large \begin{array}{llll} y = -5 x +2 \end{array}}`