Question

A bird-watcher estimates the number of songbirds to the number of birds of prey he will see on a bird-watching trip. His predictions are shown in the graph. What is the rate of change in the graph?

A. 1 /4

B. 2 /7

C. 7 /2

D. 4/ 1

Answer 1

Option B.

Explanation:

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the rate of change is

`m=(y_2-y_1)/(x_2-x_1)`

From the given graph it is clear that the graph passes through the points (0,0) and (7,2).

So, the rate of change in the graph is

`m=(2-0)/(7-0)`

`m=(2)/(7)`

The rate of change in the graph is 2/7.

Therefore, the correct option is B.

Answer 2

The rate of change of the graph is
`(2)/(7)` ⇒ answer B

Explanation:

- The graph represents a linear relation between the number of

songbird and the number of birds of prey

* x-axis represents the number of the songbirds

* y-axis represents the number of birds of prey

- The rate of change is represented by the slope of the line

- The rule of the slope of a line is:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`, where
`(x_(1),y_(1))` and
`(x_(2),y_(2))`

are two points lie on the line

- Let us find two points lie on the line from the attached figure

∵ Points (0 , 0) and (14 , 4) lie on the line

- By using the rule of the slope

∴
`m=(4-0)/(14-0)=(4)/(14)=(2)/(7)`

∵ The slope of the line represents the rate of change of the graph

∴ The rate of change of the graph is
`(2)/(7)`