Given two lines whose equations are 3x + y - 8 = 0 and -2x + by + 9 = 0, determine the value of b such that the two lines will be perpendicular.
Arrangel first line into y = mx + b form where m = slope
y = -3x +8 m = - 3 perpindicular slope = - 1/m = 1/3
arrange second equation into y=mx + b form (I'll change the 'b' in the question to 'z' to avoid confusion)
- 2x + z y = - 9
y = 2/z x - 9 / z slope 2/z = 1/3 then z = 6 (this is the 'b ' you are looking for )