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?
:
Parallel lines have equal slopes, using slope formula, we have 
{{{(3-1)/(2-a)}}} = {{{(1-10)/((a+2)-3)}}}  
{{{2/(-a+2)}}} = {{{(-9)/(a-1)}}}
cross multiply
2(a-1) = -9(-a+2)
2a - 2 = 9a - 18
2a - 9a = -18 + 2
-7a = - 16
a = {{{(-16)/(-7)}}}
a = 2.2857
:
:
Check this rather disgusting solution by finding the slope of each:
:
{{{(3-1)/(2-2.2857)}}} = {{{(2)/(-.2857)}}} ~ -7.000
and
{{{(1-10)/((2.2857+2)-3)}}} = {{{(-9)/(1.2857)}}} ~ -7.000