Question

A line passes through `(4 ,3 )` and `(1 ,4 )`. A second line passes through `(5 ,6 )`. 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: `(23,0)`

Explanation:

A line passing through `(4,3)` and `(1,4)`
has a slope of `(Delta y)/(Delta x)= (4-3)/(1-4)= -1/3`

If a line passing through `(5,6)` is parallel, it must have the same slope.

Therefore for any point `(x,y)` on this second line:
`color(white)("XXX")(y-6)/(x-5)= -1/3`
or
`color(white)("XXX")3y-18 = 5-x`
or
`color(white)("XXX")x+3y = 23`

For an easy to determine point, let `y=0`
`rarr x=23`

So another point on this second line would be `(23,0)`

graph{((x-4)^2+(y-3)^2-0.02)((x-1)^2+(y-4)^2-0.02)((x-5)^2+(y-6)^2-0.02)(x+3y-13)(x+3y-23)=0 [-5.25, 14.75, -0.626, 9.37]}