(1) A(0,2) , B(1,-0.5), C(2,-3) are the given points.

Slope of line AB = (y_{2}-y_{1})/ (x_{2}-x_{1})

= (-0.5-2)/(1-0))

= -2.5/1 = -2.5

Slope of line BC = (y_{2}-y_{1})/ (x_{2}-x_{1})

= (-3-(-0.5))/(2-1)

= -2.5/1 = -2.5

Slope of line AB and BC are equal.

Point B lies on both lines.

Point A,B,C are collinear.

(2) P(1, 2) , Q(2, 8/5 ) , R(3, 6/5 ) are the given points.

Slope of line PQ = (y_{2}-y_{1})/ (x_{2}-x_{1})

= ((8/5)-2)/(2-1))

= (-2/5)/1 = -2/5

Slope of line QR = (y_{2}-y_{1})/ (x_{2}-x_{1})

= (6/5-(8/5))/(3-2)

=( -2/5)/1 = -2/5

Slope of line PQ and QR are equal.

Point Q lies on both lines.

Point P,Q,R are collinear.

(3) L(1,2) , M(5,3) , N(8,6) are the given points.

Slope of line LM = (y_{2}-y_{1})/ (x_{2}-x_{1})

= (3-2)/(5-1))

= 1/4

Slope of line MN = (y_{2}-y_{1})/ (x_{2}-x_{1})

= (6-3)/(8-5)

=3/3 = 1

Slope of line LM ≠ Slope of MN

Point L,M,N are not collinear.