What is the difference between the net change and the averag

What is the difference between the net change and the average rate of change?

I have two points on a graph.

Point 1= (0,-1)

Point 2= (5,4)

So how do I find the net change of that and the average rate of change of those two points?

Solution

Given two points (0, -1) and (5, 4)

Let us name them as, (x₁, y_{1) and} (x₂, y₂)

Then, net change between the two points is given by, y_{2 -} y₁

y_{2 -} y_{1 = 4 - (-1) = 4 + 1 = 5}

_{Hence, required net change = 5}

Now, average rate of change between the two points is given by, (y_{2 -} y₁)/(x₂ - x₁)

(y_{2 -} y₁)/(x₂ - x₁) = (4 - (-1)) / (5 - 0)

= (4 + 1) / 5

= 5/5

= 1.

_{Hence, required average rate of change = 1.}