Determine all values of c so that the lines cy5x7 and cy3x6

Determine all values of c so that the lines cy+5x=7 and cy-3x=6 are perpendicular.

Solution

cy+5x=7

y = (-5/c)x +7/c

and cy-3x=6

y = (3/c)x +6/c

When lines are perpendicular their slope are such :m1*m2 =-1

(3/c)(-5/c) = -1

15 = c^2

c = sqrt(15) , - sqrt(15) (Solution)