Question

!20 POINTS! Which linear equation represents the data given in the table?

Answer 1

to get the equation of any straight line all we need is two points off of it, hmmm let's use (-1 , 1) and hmmmm (2 , 10)

$(\stackrel{x_1}{-1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}}\implies \cfrac{9}{2+1}\implies 3$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{3}(x-\stackrel{x_1}{(-1)}) \\\\\\ y-1=3(x+1)\implies y-1=3x+3\implies y=3x+4$