Question

A line passes through `(9 ,5 )` and `(6 ,8 )`. A second line passes through `(7 ,3 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

`(color(green)(0,10))`

Explanation:

A line passing through `(9,5)` and `(6,8)` has a slope of
`color(white)("XXX")m=(Delta y)/(Delta x) = (8-5)/(6-9)=3/(-3) =-1`

All parallel lines have the same slope.

So a parallel line passing through `(7,3)` and some other point `(x,y)` will have the form:
`color(white)("XXX")(y-3)/(x-7)=-1`
or
`color(white)("XXX")y=10-x`

Picking an arbitrary value for `x`, say `x=0`
we have
`color(white)("XXX")y=10` as a corresponding point.

So one point that satisfies the given requirements is `(0,10)`