The ratio of the parts is not k.  We calculate k this way:



That is, to find k we must add the numerator to the denominator of the
ratio of the two parts.  We plot the point and draw the line connecting them,
guessing about where P(?,?) might be:



Now we draw the run (in green) and the rise (in red):



Now we count the blocks and find that the green RUN is 6 units long
and that the red RISE is 4 units long.



Now since we know the RUN=6 and the RISE=4, and that 

k = 7/10, x1=[x-coordinate of A]=-2, y1=[y-coordinate of A]=1, we are
ready to substitute:

The x-coordinate of P is x1 + k • run = -2 + 7/10 • 6 = 

      -2 + 42/10 = -2 + 21/5 = -10/5 + 21/5 = 11/5        

The y-coordinate of P is y1 + k • rise = 1 + 7/10 • 4 = 

      1 + 28/10 = 1 + 14/5 = 5/5 + 14/5 = 19/5   


The coordinates of P are (11/5,19/5).  Final graph:



Edwin