Question

A line passes through `(2 ,8 )` and `( 1, 2 )`. A second line passes through `( 6, 1 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

One possible point would be `(12,37)`

Explanation:

A line passing though `(2,8)` and `(1,2)` has a slope
`color(white)("XXX")m=(Delta y)/(Delta x)=(8-2)/(2-1) = 6/1=6`

All parallel lines have the same slope.

So a parallel line through the point `(6,1)` would have the formula
`color(white)("XXX")(y-1)/(x-6)=6`
or
`color(white)("XXX")y-1=6(x-6)`

When `x=12` (note that this is a completely arbitrary choice)

`color(white)("XXX")y-1=6(12-6)=36`

`color(white)("XXX")y=37`