You'll need to read Zar's book to do the calculations yourself, but the basic idea is straightforward. If the P value is less than 0.05, conclude that the lines are significantly different. In that case, there is no point in comparing the intercepts. Now calculate a single slope for both lines. Now the question is whether the lines are parallel or identical.
Prism calculates a second P value testing the null hypothesis that the lines are identical.
If this second P value is high, there is no compelling evidence that the lines are different. GraphPad Prism uses this method to compare two linear regression lines. If this P value is small, you conclude that the treatment made a difference overall.