Question

The graph shows the girth, in cm, of the trunk of a fir tree after different numbers of years:(Graph image may be below)

What does the slope of the graph represent?

A)The girth increases by 7 centimeters each year.
B)The girth increases by 5 centimeters each year.
C)The original girth was 5 centimeters.
D)The original girth was 7 centimeters.

Answer 1

Option A is correct.

the girth increases by 7 cm each year.

Explanation:

Let y axis represents the girth in cm of the trunk of a fir tree and

x axis represents time in years.

Using the formula for slope : For any two points
`(x_1 , y_1)` and
`(x_2 , y_2)` the slope of the line(m) is given by:

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

From the graph:

Take any two points to find the slope of the line:

Let two points be (0, 5) and (5, 40)

Then, by the formula of slope:

`m =(40-5)/(5-0)=(35)/(5)` = 7.

Therefore, The girth increases by 7 centimeters each year.

Answer 2

This is a linear function: y = mx + b, where m = slope and b, the value of y when x = 0

Having said that, the equation becomes : y = 7x+5

And the slope of the graph represents : A)The girth increases by 7 centimeters each year