Question

Find the equation of the linear function represented by the table below in slope-intercept form.

x y
-4 17
1 -3
6 -23
11 -43

Answer 1

well, to get the equation of a line all we need is two points, so let's simply pick two points off the table, hmmmm say (1 , -3) and hmmm (11 , -43)

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{11}~,~\stackrel{y_2}{-43}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-43}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{11}-\underset{x_1}{1}}}\implies \cfrac{-43+3}{10}\implies \cfrac{-40}{10}\implies -4`

`\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}{(-3)}=\stackrel{m}{-4}(x-\stackrel{x_1}{1}) \\\\\\ y+3=-4x+4\implies y=-4x+1`