Question

What is the following linear function of a graph that contains the points of (0,0),(1,4),(2,1)?

Answer 1

The points do not lie along a straight line.

Explanation:

3 Points that lie along the same line are said to be "collinear" and collinear points must have the same slope between any pair of points.

I shall label the points `A, B, and C`

`A = (0,0),B = (1,4),C =(2,1)`

Consider the slope from point A to point B:

`m_"A-B"= (4-0)/(1-0) = 4`

Consider the slope from point to point C:

`m_"A-C" = (1-0)/(2-0) = 1/2`

If points A, B and C were collinear, then `m_"A-B"` would equal `m_"A-C"` but they are not equal, therefore, they are not collinear.