Find a relation between x and y if the points (x,y), (1,2) and (7,0) are collinear.

The given points are collinear then the area of triangle formed by these points will be 0
∴1/2[x1(y2−y1)+x2(y3−y1)+x3(y1−y2)]=0
Here (x1,y1)=(x,y) (x2,y2)=(1,2) (x3,y3)=(7,0)
⇒1/2[x(2−0)+1(0−y)+7(y−2)]=0
⇒1/2[2x−y+7y−14]=0
⇒1/2[2x+6y−14]=0
⇒2x+6y−14=0
⇒x+3y−7=0
Hence this is the required relation between x and y.