Question

A line passes through `(9 ,2 )` and `( 3, 5 )`. A second line passes through `( 4, 8 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

It can be any point on the second line, for example (0,10) as explained below.

Explanation:

The slope of the line passing though (9,2) and (3,5) would be `(5-2)/(3-9)= (3)/(-6) = -1/2`.

The slope of the second line would also be `- 1/2` because it is parallel to the first one. Second line also passes through the point (4,8), hence its equation in point slope form would be `y-8= -1/2 (x-4)`. Another point on this line can be any, which can be obtained by assigning any arbitrary value to x and finding the corresponding y. For example, let x=0, then y=10. Hence this point point would be (0,10)