How can you use the point-slope form of a line when only given two points?

If we already have two points of the line, we can find its slope (), its intersection with the y-axis (), hence its point-slope form equation in the following way:

Let's call Point 1:  and Point 2:

The Slope equation is:

Now, the equation of the line in its point-slope form is:

And we can find the intersection with the y-axis () by evaluating the equation with any of the two given points and then isolating .