If the line passing through the points (a, 1) and (2, 6) is parallel to the line passing through the points (−8, 9) and (a + 2, 1), what is the value of a?

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lemjay | High School Teacher | (Level 3) Senior Educator

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To solve , we need to take note that the parallel lines have the same slope. So, determine the slope of each line.

For the line passing through the points (a,1) and (2,6), its slope is:

`m_(L1)=(y_2-y_1)/(x_2-x_1)=(6-1)/(2-a)`

`m_(L1)=5/(2-a)`

And for the other line passing through the points (-8,9) and    (a+2, 1), its slope is:

`m_(L2)=(y_2-y_1)/(x_2-x_1)=(1-9)/(a+2-(-8))=(-8)/(a+10)`

`m_(L2)=-8/(a+10)`

Now that the slope of each lines are known, set the equal to each other.

`m_(L1)=m_(L2)`

`5/(2-a)=-8/(a+10)`

Then, solve for a.

`5*(a+10)=-8*(2-a)`

`5a+50=-16+8a`

`5a-8a=-16-50`

`-3a=-66`

`a=22`

Hence, the value of a is 22.

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