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

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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(39630) About Me  (Show Source):
You can put this solution on YOUR website!
"Parallel", indicates slopes are equal.

%288-1%29%2F%281-a%29=%281-5%29%2F%28a%2B2-12%29

7%2F%281-a%29=-4%2F%28a-10%29

Conitnue.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If the line passing through the points
(a, 1) and (1, 8)
and parallel to the line passing through the points
(12, 5) and (a+%2B+2,+1)
to find equations, start with slope-intercept form and find a slope and y-intercept:
y=mx%2Bb use point (1, 8)
8=m%2A1%2Bb+
8=m%2Bb
m=8-b............eq.1
for parallel line:
y=mx%2Bb use point (12, 5)
5=m%2A12%2Bb
5=12m%2Bb
12m=5-b
m=%285-b%29%2F12...........eq.2
the parallel line will have same slope: so, we have
8-b=%285-b%29%2F12.....solve for b
96-12b=5-b
96-5=12b-b
91=11b
b=91%2F11
then slope of the first line is:
m=8-b => m=8-91%2F11=88%2F11-91%2F11=-3%2F11
and equation of first line is:

y=-%283%2F11%29x%2B91%2F11 use point (a, 1) to find a
1=-%283%2F11%29a%2B91%2F11 ..........solve for a
%283%2F11%29a=91%2F11-1
3a%2F11=91%2F11-11%2F11
3a%2F11=80%2F11 ...if denominators same then
3a=80
a=80%2F3
or
a=26.66666666666667
a=26.7=> the point is (a, 1)=(26.7, 1)


find second equation:
slope is same m+=-3%2F11 find b
-3%2F11+=%285-b%29%2F12
-%283%2F11%2912=5-b
b=36%2F11

so, second equation is:
y=-%283%2F11%29x%2B3.27 use point (a+%2B+2, 1)
1=-%283%2F11%29%28a+%2B+2%29%2B3.27
1-3.27=%28-3%2F11%29%28a+%2B+2%29
-2.27%2F%28-3%2F11%29=a+%2B+2
2.27%2F0.27=a+%2B+2
8.4=a%2B2
a=8.4-2
a=6.4 => the point is (a+%2B+2,+1)=(6.4+%2B+2, 1)=(8.4, 1)



Answer by MathTherapy(10557) About Me  (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: %288+-+1%29%2F%281+-+a%29, or 7%2F%281+-+a%29

Line with points (12, 5) and (a + 2, 1) has slope: %281+-+5%29%2F%28a+%2B+2+-+12%29, or %28-+4%29%2F%28a+-+10%29

Since the lines are parallel, their slopes will be equal, and so: 

7%2F%281+-+a%29+=+%28-+4%29%2F%28a+-+10%29

7(a – 10) = - 4(1 – a) ------ Cross-multiplying

7a – 70 = - 4 + 4a

7a – 4a = - 4 + 70

3a = 66

a = 66%2F3, or highlight_green%2822%29

You can do the check!! 

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