Answer
$ y-3=1(x-1)\qquad$ ... point-slope form
$y=x+2 \qquad$ ... slope-intercept form
$f(x)=x+2 \qquad$ ... function notation
Work Step by Step
$(x_{1},y_{1})=(1,3) \; (x_{2},y_{2})=(2,4)$
$m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{4-3}{2-1}=\frac{1}{1}=1$.
So with $m=1$ and $(x_{1},y_{1})=(1,3)$, we write the point-slope form
$y-y_{1}=m(x-x_{1})$
$ y-3=1(x-1)\qquad$ ... point-slope form
Simplify to slope-intercept form, $ y=mx+b$
$ y-3=x-1\qquad$... add 3
$ y=x+2 \qquad$ ... is the slope-intercept form
For function notation, replace $y$ with $f(x)$.
