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 .
+23246 To find the equation of the line that passes through (7,8) and (9,0)
has a slope of (0 - 8)/(9-7) = -8/2 = -4
The equation of this line is: y - 0 = -4(x - 9) ---> y = -4x + 36
Finding where these two lines intersect: y = 2x - 10 and y = -4x + 36
---> 2x - 10 = -4x + 36
6x = 46
x = 7 2/3
and y = 5 1/3
Adding these two values give you a sum of 13.
