SOLUTION: If the line passing through the points (a, 1) and (2, 3) is parallel to the line passing through the points (3, 10) and (a + 2, 1), what is the value of a?

Algebra ->  Linear-equations -> SOLUTION: If the line passing through the points (a, 1) and (2, 3) is parallel to the line passing through the points (3, 10) and (a + 2, 1), what is the value of a?      Log On


   

Question 451340: If the line passing through the points (a, 1) and (2, 3) is parallel to the line passing through the points (3, 10) and (a + 2, 1), what is the value of a?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If the line passing through the points (a, 1) and (2, 3) is parallel to the line
passing through the points (3, 10) and (a + 2, 1),
what is the value of a?
:
Parallel lines have equal slopes, using slope formula, we have
%283-1%29%2F%282-a%29 = %281-10%29%2F%28%28a%2B2%29-3%29
2%2F%28-a%2B2%29 = %28-9%29%2F%28a-1%29
cross multiply
2(a-1) = -9(-a+2)
2a - 2 = 9a - 18
2a - 9a = -18 + 2
-7a = - 16
a = %28-16%29%2F%28-7%29
a = 2.2857
:
:
Check this rather disgusting solution by finding the slope of each:
:
%283-1%29%2F%282-2.2857%29 = %282%29%2F%28-.2857%29 ~ -7.000
and
%281-10%29%2F%28%282.2857%2B2%29-3%29 = %28-9%29%2F%281.2857%29 ~ -7.000