Question

f the line passing through the points (1, a) and (5, −2) is parallel to the line passing through the points (2, 8) and (−5, a + 7), what is the value of a?

Answer 1

`a=-6`

Explanation:

Line 1: (1, a) and (5, −2)

slope of the line is

`slope = (y_2-y_1)/(x_2-x_1) =(-2-a)/(5-1) =(-2-a)/(4)`

Line 2: (2, 8) and (−5, a + 7)

slope of the line is

`slope = (y_2-y_1)/(x_2-x_1) =(a+7-8)/(-5-2) =(a-1)/(-7)`

when the lines are parallel then slopes are equal

`(a-1)/(-7) =(-2-a)/(4)`

cross multiply it

`4(a-1)=-7(-2-a)`

`4a-4=14+7a`

subtract 4a from both sides

`-4=14+3a`

`-18=+3a`

divide both sides by 3

`a=-6`