Question

Determine whether the three points A(-2,-1), B(0,4) and C(2,9) all line on the same line.

Answer 1

All three of them do exist on the line y = 2.5x + 4

In order to find the answer to this question, start by finding the line for two points. For this example, we'll use A and C. 

First we need to find the slope. 
(y1 - y2)/(x1 - x2)
(9 - -1)/(2 - -2)
(9 + 1)/(2 + 2)
10/4
2.5

Now using slope intercept form and point A, we can determine the intercept of that line as well. 

y = mx + b
-1 = 2.5(-2) + b
-1 = -5 + b
4 = b

So now we know A and C form the line y = 2.5x + 4. We can then check if B fits that line. 

y = 2.5x + 4
4 = 2.5(0) + 4
4 = 0 + 4
4 = 4 (TRUE)

Therefore, it also falls on that line.