Assuming:

y – x +2 = 0 divides the line joining the points (3, -1) and (8, 9) at the point P in the ratio k : 1

To prove:

Line y - x + 2 = 0 divides the join of points (3,-1) and (8, 9) in the ratio 2:3

Explanation:

P

P lies on the y – x +2 = 0

Therefore,

⇒ -1 + 9k – 3 – 8k +2k + 2 = 0

⇒ 3k = 2

⇒ k

Hence Proved, the line y – x +2 = 0 divides the line joining the points (3, -1) and (8, 9) in the ratio 2 : 3