Two points define a line and a line can be represented as a linear equation in several forms.

The Point-Slope form

The Slope-Intercept form

The General Form

The equations for solving for all forms are shown.
This applet allows you to move two points around the plane and see the resulting equations in the three different forms.

Generally, one form can be converted into another form with a little algebra. There is one case where this is not true.
Can you find the case where algebra does not allow you to convert equation forms?
Which derived term appears directly in two of the forms?
Which form above has some simplification applied to the resulting equation?