Multiple regression

I am a bit confused with multiple regression.

I understand every predictor will lead to different Y values and will create different linear lines on the graph. I know that this will in turn lead to different slopes of the lines (b values). But when you form the equation there is only one intercept (e.g. 'a') that is used...

Is this basically because the slopes of the line will all cross the y axis at the same point, and how is this possible? Sorry if this is a silly question!