Question

find the relation between X and Y if the points (x,y),(1,2),(7,0) are collinear

Answer 1

slope of every 2 points will be equal
$(2 - y) \div (1 - x) = - 2 \div 6 = - y \div (7 - x)$
solve

Answer 2

Since the condition here is that the three ponits are collinear, therefore the three points will surely will not make a triangle.. or in others words area of triangle formed by them is equal to 0.
A/Q
1/2| {x(2-0)+1(0-y)+7(y-2)} | = 0
ie, 2x-y+7y-14=0
ie, 2x+6y=14
ie, x+3y-7=0