Answer
Please see the notes below.
Work Step by Step
$ y - y_{1} = m (x - x_{1})$ (starting in point slope form)
$ y - y_{1} = m*x - m*x_{1}$ (expanding the right side of the equation)
$ y - y_{1} = mx - mx_{1}$ (simplifying the right side of the equation)
$ y - y_{1} (+y_{1}) = mx - mx_{1} (+y_{1})$ (adding y_{1} to both sides to solve for y)
$ y = mx - mx_{1} +y_{1} $
$m, x_{1}$, and $y_{1}$ are all numbers (constants), so we can calculate the combined value of these constants. Let $b$ be the sum of $mx_{1} +y_{1}$. Thus, we can make the following conversion.
$ y = mx - mx_{1} +y_{1} $
$ y = mx (- mx_{1} +y_{1}) $
$ y = mx + b $
