# Are These 3 Points Collinear?

On the topic of groovy math, here’s some smooth algebra.

Given 3 points, are these points collinear?

Collinear means the points will all be on the same line. If this is the case, then all the points would satisfy an equation y=mx+b. If they are all on the same line, then they will all have the same slope (m) and same y-intercept (b).

For example: Given points (1,-1), (3,3) and (0,3)

y=mx+b
-1=1m+b

m=change in y/change in x
m= (-1-3)/(1-3)= -4/-2=2

-1=1(2)+b
-1=2+b
b=-1-2=-3

y=2x-3

Plug points in to see if they fit the equation.
-1=2(1)-3 yup
3=2(3)-3 yup
3=2(0)-3 nope!

Since (0,3) does not satisfy the equation, then the three given points are not collinear.