Question

In a paragraph, compare and contrast constant rate of change and average rate of change.

Answer 1

Constant Rate of change: Constant Rate of change means the object is moving with a constant velocity and the curve will be linear.We have to  find the slope of a linear function.In constant rate of change if you will take any two ponts on the curve and find it's slope the slope will be same. i. Suppose there is a line which passes through (2,2) and (4,4).To find the constant rate of change we just need to join these points and just use the formula of finding the slope of line joining two points.

$(x_{1},y_{1}), (x_{2},y_{2}) \text  { is }  \frac{y_{2}- y_{1}}{x_{2}- x_{1}}=\frac{y-y_1}{x-x_1}$

By using this Formula you can find the equation of a linear function also.

And if you take any two points on this line and and will find the slope ,the slopes will be same.

The equation of linear function is y=a+bx

2. Average rate of change⇒ In average rate of change we find the equation of a secant line.you have read that a secant line is the line which cuts the curve at two points. To find the average rate of change between two points

$(x_{1},y_{1}), (x_{2},y_{2}) \text { is }\\ \frac{y_2-y_1}{x_2-x_1}$

So when you talk about constant rate of change we are taking about finding the slope of a linear function for which slope  is same everywhere  and when we talk about  Average rate of change we are finding the slope of a secant line i.e line joining any two points on the curve.The slope is not same  if you join any other two points.