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.
+128474 Find the slope of the second line
( 8 - 0 ) / ( 7 - - 9) = 8 / 16 = 1/2
Using ( -9, 0) the equation of this line =
y = (1/2) ( x - - 9)
y = (1/2)x + 9/2
Set the y's equal
2x -10 = (1/2) x + 9/2 multiply through by 2
4x - 20 = x + 9
3x = 29
x = 29/3
And y = 2 ( 29/3) -10 = 28/3
(a , b) = ( 29/3 , 28 /3)
(a + b) = 29/3 + 28/3 = 57 / 3 = 19
