slope intercept equation

Question

the graph of f passes through (-6,9) and is perpendicular to the line that has an xintercept of 6 and y intercept of -18

the equation of the function is ???

Answer 1

x intercept of 6 and y intercept of -18

means the two points (6,0) and (0,-18)

a line through those two points is (0--18)/(6-0) = y/(x-6) = 3

y = 3x -18. The slope of a perpendicular line is the negative inverse of 3, = -1/3

y = -x/3 + b. plug in the point (-6, 9) to solve for b

9= 6/3 + b

b = 7

y = -x/3 + 7 is the perpendicular line through the given point

f(x) = -x/3 + 7