Problem 8 of my hw Linear algebra Determine if points are co

Problem 8 of my hw. Linear algebra. Determine if points are collinear.

Determine whether the points are collinear. If so, find the line y = c_0 + c_1x that fits the points. (If the points are not collinear, enter NOT COLLINEAR.) (0, 1), (1, 4), (2, 7)

Solution

if points are collinear then slope of any two points would be same .

(0, 1) (1,4) and ( 2, 7)

m1 = (4 -1)/(1-0) = 3

m2 = (7-4)/(2-1) =3

Hence points are collinear

Line : y = co +c1x

c1 = slope = 3 : y = co +3x

find co from (0,1)

1 = c0

So, y = 1 +3x