Let P=(a,b) be the point of intersection of the line y=2x-10 and the line through (7,8) and (9,0). Compute a+b.

The line through (7,8) and (9,0) can be written as y = mx + c, where m and c are constants found from the following:

8 = 7m + c

0 = 9m + c

Hence 2m = -8 or m = -4, so c = 8 + 7*4 = 36

Therefore the line is described by  y = -4x + 36

Now equate this and y = 2x - 10 to find the values of x (=a) and y (=b) that satisfy both equations.