A line goes through the points A and B.
Move point A or point B to see how the position of point C changes.
Also note the value of the slope as you move point A or B.

Did you notice that point C stayed on the -axis? Even when point C was out of view?
Did you notice that the -value of point C is the same value of the constant in the linear equation?
Did you notice how the value for the slope changed as you moved either point?
Did you notice that the value for the slope is the same value for the coefficient of in the line equation?