Question

What is an equation of the line in point-slope form? How can the point-slope form be written in function notation?

Answer 1

The equation of a line in point slope form = $y - y_1 = m(x - x_1)$

To put $y - y_1 = m(x - x_1)$ into function notation, we need to get y by its self.
Lets say we had a point (2,2) and a slope of 3. Ok, now that we have our point and slope, lets turn point slope form into  function notation.

$y - y_1 = m(x - x_1)$
$y - 2 = 3(x - 2)$
$y - 2 = 3x - 6$
$y = 3x - 6 + 2$
$y = 3x - 8$
Change the y to f(x)
$f(x) = 3x - 8$      <-----Function notation.