Question

Write an equation in the form y=mx +b to represent each table

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}{0}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{16}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{16}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{12}-\underset{x_1}{0}}} \implies \cfrac{ 16 +8 }{ 12 } \implies \cfrac{ 24 }{ 12 } \implies 2`

`\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}{2}(x-\stackrel{x_1}{0}) \implies y +8 = 2 ( x -0) \\\\\\ y+8=2x\implies {\Large \begin{array}{llll} y=2x-8 \end{array}}`