If the line passing through the points (a, 2) and (6, 7) is parallel to the line passing through the points (4, 8) and (a + 3, 2), what is the value of a?

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The answer :

we know the line pass through (a,2) and (6,7) so the equation of the line is :

y = mx + b to find m = (7-2)/(6-a) = 5/(6-a)

ane the other line pass through (4,8) and (a+3,2) so the equation of the line is :

y = nx + c to find n = (8-2)/(4-a-3) = 6/(1-a)

and we know the two line is parallel so n = m

so : 5/(6-a) = 6/(1-a)

so : 5(1-a) = 6(6-a)

so: 5 - 5a = 36 - 6a

so : 6a - 5a = 36 - 5

so : a = 31

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