Question

A line passes through `(5 ,1 )` and `(6 ,5 )`. A second line passes through `(1 ,3 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

One other point that satisfies these conditions is `(2,8)`

Explanation:

The slope of a line through `(5,1)` and `(6,5)`
is `(Deltay)/(Deltax)=(5-1)/(6-5)=5/1`

A line through`(1,3)` parallel to this first line must have the same slope.

As long as the ratio `Deltay:Deltax` is maintained
`(1+Deltax,3+Deltay)` will be a valid point on this second line.

Some possibilities that maintain this ratio:
`color(white)("XXX")(Deltax,Deltay)=(1,5)color(white)("XX")rarrcolor(white)("XX")"point:"(1+1,3+5)=(2,8)`

`color(white)("XXX")(Deltax,Deltay)=(2,10)color(white)("XX")rarrcolor(white)("XX")"point:"(1+2,3+10)=(3,11)`

`color(white)("XXX")(Deltax,Deltay)=(-1,-5)color(white)("XX")rarrcolor(white)("XX")"point:"(1+(-1)1,3+(-5))=(0,2)`