The set of points collinear

Question

The set of points (-2, 1), (0, 3), (2, 5) is collinear.or not?

Answer 1

Given points are (-2, 1) =(x1, y1), (0, 3) = (x2, y2) and (2, 5)

Since any 2 points determine 1 line, take 2 of the points and find the equation of the line drawn through these 2

points.

=>Slope = (y2-y1) ÷ (x2 - x1) 

                 = (3 - 1) ÷ (0 + 2)

                 = 2/2 = 1

y = slope * x + b

Substitute the x and y of the third point (2, 5) into the equation and find the y-intercept (b)

=> y = (1)x + b      

=> 5 = 2 + b

=> b = 5-2

         = 3

y =  x + 3

By checking the point  (-2, 1) we get,

1 = -2 +3

1 = 1

By checking the point  (0, 3) we get,

3 = 0 + 3

3 = 3

By checking the point  (2, 5) we get,

5 = 2 + 3

5 = 5

Therefore the three points are collinear which lie on the same line.