Question

Find the equation of the linear function represented by the table below 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}{-1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{ -4 }{3 +1} \implies \cfrac{ -4 }{ 4 } \implies -1`

`\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}{-1}(x-\stackrel{x_1}{(-1)}) \implies y -5 = -1 ( x +1) \\\\\\ y-5=-x-1\implies {\Large \begin{array}{llll} y=-x+4 \end{array}}`