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

Answer:

Option B.

Step-by-step explanation:

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

$m=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{2-0}{7-0}$

$m=\frac{2}{7}$

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

Therefore, the correct option is B.

Answer 2

Answer:

The rate of change of the graph is $\frac{2}{7}$ ⇒ answer B

Step-by-step 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:

  $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$, 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

∴ $m=\frac{4-0}{14-0}=\frac{4}{14}=\frac{2}{7}$

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

∴ The rate of change of the graph is $\frac{2}{7}$