Line a passes through points (1, 12) and (9, 3). line b is perpendicular to a. what is the slope of line b?

(x₁, y₁) = (1,12)
(x₂, y₂) = (9,3)

Find slope of line a
m = (y₂ - y₁)/(x₂ - x₁)
m = (3-12)/(9-1)
m = -9/8

Find slope of line b
m₁ × m₂ = -1
-9/8 × m₂ = -1
m₂ = 8/9

Slope of line b is 8/9

Find the slope of line a.

m= (y2-y1)/(x2-x1)

m= (3-12)/(9-1)

m= (-9)/8

Flip the fraction and the sign for the perpendicular slope.

8/9 <- the perpendicular slope

I hope this helps!
~kaikers