Chapter 5.1, Problem 1P

Determine whether each rate of change is constant. If it is, find the rate of change and explain what it represents.

To determine

To calculate : rate of change if it is constant. Also, to find what rate of change represents.

Answer to Problem 1P

Rate of change is 2.

It represents change in number of goals with respect to increase in number of games

Explanation of Solution

Given information:

The following table is given:

Games	Goals
1	2
2	4
3	6

Formula used: For two points $\left(x_1,y_1\right),\left(x_2,y_2\right)$ , rate of change is given by $\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Games	Goals
1 $(x_1)$	2 $(y_1)$
2 $(x_2)$	4 $(y_2)$
3 $(x_3)$	6 $(y_3)$

Take $\left(x_1,y_1\right)=\left(1,2\right),\left(x_2,y_2\right)=\left(2,4\right)$

So,

Rate of change $(R_1)=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{2-1}=\frac{2}{1}=2$

Take $\left(x_2,y_2\right)=\left(2,4\right),\left(x_3,y_3\right)=\left(3,6\right)$

So,

Rate of change $(R_2)=\frac{y_3-y_2}{x_3-x_2}=\frac{6-4}{3-2}=\frac{2}{1}=2$

As $R_1=R_2$ , rate of change is constant.

Hence,

Rate of change $=R_1=R_2=2$

Also, rate of change represents change in number of goals with respect to increase in number of games