SOLUTION: If the line passing through the points (a, 1) and (15, 6) is parallel to the line passing through the points (14, 7) and (a + 2, 1), what is the value of a?

Algebra ->  Linear-equations -> SOLUTION: If the line passing through the points (a, 1) and (15, 6) is parallel to the line passing through the points (14, 7) and (a + 2, 1), what is the value of a?      Log On


   

Question 710243: If the line passing through the points
(a, 1) and (15, 6)
is parallel to the line passing through the points
(14, 7) and (a + 2, 1),
what is the value of a?
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Use the slope formula:



where and are the coordinates of the given points.

to calculate the slope of the first line in terms of . Then do the same thing for the other two points. Since parallel lines have equal slopes, set the two fractions equal to each other and then solve for

John

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Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Find the slope of the first line using the slope formula:

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

where (x1,y1) = (a,1)

and where (x2,y2) = (15,6)

m = %286-1%29%2F%2815-a%29

m = 5%2F%2815-a%29

Find the slope of the second line using the slope formula:

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

where (x1,y1) = (14,7)

and where (x2,y2) = (a+2,1)

m = %281-7%29%2F%28%28a%2B2%29-14%29

m = -6%2F%28a%2B2-14%29

m = -6%2F%28a-12%29

Since they are parallel their slopes are equal, so we 
set the two slopes equal:

5%2F%2815-a%29 = -6%2F%28a-12%29

Cross multiply and solve and get a=30

Edwin