Question

Do the three points lie on one line?

(5,6), (3,2), (6,8)
Also, should I do this on graph paper?​

Answer 1

Yes. No graph paper.

Explanation:

Let's say the 3 points are A, B, C.

If A, B and C lie on one line then
`m_(AB) = m_(BC) = m_(AC)`

`m_(AB) = (y_(B)-y_(A) )/(x_(B)-x_(A)) = (2-6)/(3-5) = (-4)/(-2) = 2\\m_(BC) = (y_(C)-y_(B) )/(x_(C)-x_(B)) = (8-2)/(6-3) = (6)/(3) = 2\\\\m_(AC) = (y_(C)-y_(A) )/(x_(C)-x_(A)) = (8-6)/(6-5) = (2)/(1) = 2\\\\`

Hence, they lie on one line.

You don't need to use a graph paper to prove it.