Changes

<math> y - y' = \frac{dy}{dx}\ x - x'</math>

<math> y - y' = \frac{dy}{dx}\ x - x'</math>

When one point on the curve is known, x and y values are plugged into <math> \frac{dy}{dx}\ </math> to find the slope at a particular point, and the coordinates of the point are plugged in for <math> (x',y') </math>

When <math> (x',y') </math> is a known point on the line.