Question

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

Answer 1

okay, let's switch these both into y=mx+b form, because its a little easier to visualize slope that way.
we get the first line: y=-(5/c)x+7/c, and the 2nd line we get y=(3/c)x+6/c.

the only qualification for two lines to be perpendicular is that the slope of one is equal to the negative reciprocal of the other
(the reciprocal of n is (-1/n) for example)

so, (-5/c) must be equal to -1/(3/c). we simplify both and we get

-5/c = -c/3. we multiply both sides by c

and get
-5=-(c^2)/3

multiply both sides by -3

and we get that 15=c^2
so c= +/- \[\sqrt{15}\]

Answer 2

@JHall96 Thank you so much!