Question

The height of a birch tree, f(x), in inches, after x months is shown in the graph below.

How much does the birch tree grow per month, and what will be the height of the birch tree after 10 months?

A. The birch tree grows 1 inch per month. The height of the birch tree will be 16 inches after 10 months.

B. The birch tree grows 2 inches per month. The height of the birch tree will be 26 inches after 10 months.

C. The birch tree grows 3 inches per month. The height of the birch tree will be 36 inches after 10 months.

D. The birch tree grows 2 inches per month. The height of the birch tree will be 24 inches after 10 months.

Answer 1

look at the slope of the line(aka rise over run)
For every 1 month, the sapling grows 2 inches

answer: D

Answer 2

The correct option is B.

Explanation:

The slope intercept form of a line is

`y=mx+b`

Where, m is slope and b is y-intercept.

if a line passing thorough two point then the slope of the line is

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

The line passing through the point (0,6) and (1,8), so the slope of the lien is

`m=(8-6)/(1-0)=2`

The slope of line is 2, it means the birch tree grows 2 inches per month.

From the given graph it is clear that the y-intercept of the line is 6 and the slope is 2. So, the equation of line is

`y=2x+6`

Put x=10.

`y=2(10)+6=26`

The height of the birch tree will be 26 inches after 10 months.

Therefore, the correct option is B.