Using slopes show that the points A

For three points to be collinear, the slope of all pairs must be equal, that is the slope of AB = slope of BC = slope of CA

Given points are A(6, -1), B(5, 0) and C(2, 3)

slope $=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)$

Slope of $A B=\left(\frac{0+1}{5-6}\right)=\frac{1}{-1}=-1$

Slope of $B C=\left(\frac{3-0}{2-5}\right)=\frac{3}{-3}=-1$

Slope of $C A=\left(\frac{3+1}{2-6}\right)=\frac{4}{-4}=-1$

Therefore slopes of AB, BC and CA are equal, so Points A,B,C are collinear.