SOLUTION: A line passing through the points (2a+2,3a^2) and (3a+4,5a^2) has a slope of a+3. Find all possible values of a.

Algebra ->  Inequalities -> SOLUTION: A line passing through the points (2a+2,3a^2) and (3a+4,5a^2) has a slope of a+3. Find all possible values of a.      Log On


   

Question 1035766: A line passing through the points (2a+2,3a^2) and (3a+4,5a^2) has a slope of a+3. Find all possible values of a.
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
We would write, using the formula for the slope
m+=+a+%2B+3+=+%285a%5E2-3a%5E2%29%2F%28%283a%2B4%29-%282a%2B2%29%29
which simplifies to
a+%2B+3+=+2a%5E2+%2F%28a%2B2%29
Multiply by a+2, we get
a%5E2+%2B+5a+%2B+6+=+2a%5E2
Rearranging we get
a%5E2+-+5a+-+6+=+0
%28a-6%29%28a%2B1%29+=+0
and
a = 6 or a = -1