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

`color(green)(""(20,0))`

Explanation:

The slope of the first line through `(9,2)` and `(3,5)` is
`color(white)("XXX")color(green)(m)=(Deltay)/(Deltax)=(5-2)/(3-9) = color(green)(-1/2)`

A second line through `(4,8)` parallel to the first line must also have a slope of
`color(white)("XXX")color(green)(m)=color(green)(-1/2)`
That is
`color(white)("XXX")color(green)(m)=(bary-8)/(barx-4)=color(green)(-1/2)`
for all points `(barx,bary)` on the second line.
`rarrcolor(white)("XXX")2bary-16=4-barx`

`rarrcolor(white)("XXX")barx= 20-2bary`

To find a point on the second line pick an arbitrary value for `bary` and solve for `barx`
For example, if `bary=0`
`color(white)("XXX")barx=20-2 * 0 = 20`
giving us the point `(20,0)` on the second line.