Answer
The equation of the line is $y=2x+1$
Work Step by Step
$(x_{1},y_{1})=(2,5)$
$(x_{2},y_{2})=(4,9)$
Find the slope of the line: $m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
$m=\displaystyle \frac{9-5}{4-2}=\frac{4}{2}=2$
You know the slope and a point on the line, so use point-slope form with either
given point to write an equation of the line. Choose $(x_{1},y_{1})=(2,5).$
$ y-y_{1}=m(x-x_{1})\qquad$ ...substitute $5$ for $y_{1},\ 2$ for $m$ and $2$ for $x$.
$ y-5=2(x-2)\qquad$ ...apply the Distributive Property.
$ y-5=2x-4\qquad$ ...add $5$ to each side.
$y=2x+1$
