Question

Find the value of a if the lines ax+3y=5 and 2x+(a+1)y=6 are parallel.

Answer 1

parallel means equal slopes :

3y = 5 - ax
y = (5/3)- (ax/3)
so slope -a/3

2x + (a+1)y = 6
(a+1)y = 6 - 2x
y = (6/(a+1)) - 2x/(a+1)
so slope -2/(a+1)

now you have to equate them :

-2/(a+1) = -a/3

6 = a(a+1)

a^2 + a -6 = 0
a^2 +3a -2a -6 = 0
a(a+3) -2 (a+3)
(a-2)(a+3) = 0
a = 2, -3

Answer 2

Thanks :) i forgot a step

Answer 3

How would you mathematically find the perpendicular?