SOLUTION: If the line passing through the points (a, 1) and (1, 8) is parallel to the line passing through the points (12, 5) and (a + 2, 1), what is the value of a? a = please show al

Question 936106: If the line passing through the points
(a, 1) and (1, 8)
is parallel to the line passing through the points
(12, 5) and (a + 2, 1),
what is the value of a?
a =
please show all work
Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
"Parallel", indicates slopes are equal.

Conitnue.

Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
If the line passing through the points
(, ) and (, )
and parallel to the line passing through the points
(, ) and (,)
to find equations, start with slope-intercept form and find a slope and y-intercept:
use point (, )

............eq.1
for parallel line:
use point (, )

...........eq.2
the parallel line will have same slope: so, we have
.....solve for

then slope of the first line is:
=>
and equation of first line is:

use point (, ) to find
..........solve for

...if denominators same then

or

=> the point is (, )=(, )

find second equation:
slope is same find

so, second equation is:
use point (, )

=> the point is (,)=(, )=(, )

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

If the line passing through the points
(a, 1) and (1, 8)
is parallel to the line passing through the points
(12, 5) and (a + 2, 1),
what is the value of a?
a =
please show all work

Line with points (a, 1) and (1, 8) has slope: , or
Line with points (12, 5) and (a + 2, 1) has slope: , or
Since the lines are parallel, their slopes will be equal, and so:

7(a � 10) = - 4(1 � a) ------ Cross-multiplying
7a � 70 = - 4 + 4a
7a � 4a = - 4 + 70
3a = 66
a = , or
You can do the check!!
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