Question

The coordinate pairs (-5, -11), (0, -1), and (5, 9) are solutions to which function?

Answer 1

Find out the slopes with each of the three points.
\[Slope=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]\[Slope=\frac{-1-(-11)}{0-(-5)}=\frac{10}{5}=\frac{2}{1}\]\[Slope=\frac{9-(-1)}{5-0}=\frac{10}{5}=\frac{2}{1}\]\[Slope=\frac{9-(-11)}{5-(-5)}=\frac{20}{10}=\frac{2}{1}\]so the slopes between all the points are the same, so the function is linear.
now to find out the function y=mx+b is easy.
m(slope)=2 b(y-intercept)=0 (because one of the coordinates is (0,-1))
so function is y=2x-1