Line through (0,b) and (10,-5) is perpendicular to the line through (a,0) and (-6,-3). If all ordered pairs (a,b) which make the first sentence of this problem true are graphed, they all lie on a line. Find the equation of this line.

Answer 1

We have two lines, with slopes

(-5-b)/10 and (-3)/(-6-a)

If the lines are perpendicular, then

(-5-b)/10 * (-3)/(-6-a) = -1
(b+5) = 10/3 (a+6)
b = 5/3 (2a+9)