Question

The table of values below represents a linear function and shows the height of a tree since it was transplanted. What was the height of the tree when it was transplanted?

Answer 1

4 feet is the answer

Answer 2

The height of the tree when it was transplanted was:

4 feet

Explanation:

As we could observe that the given table represents a linear function.

The table is given as follows:

Year since it was 4 4.5 5

transplanted

Height (Feet) 12 13 14

We will find the linear function.

Let y denotes height and x denote year since it was transplanted.

We know that any linear function passing through two points (a,b) and (c,d) is given by:

`y-b=(d-b)/(c-a)* (x-a)`

Here let (a,b)=(4,12) and (c,d)=(5,14)

Hence, the linear function is calculated as follows:

`y-12=(14-12)/(5-4)* (x-4)\\\\\\y-12=2(x-4)\\\\\\y-12=2x-8\\\\\\y=2x-8+12\\\\\\y=2x+4`

Now the height of tree when it was transplanted is the value of y when x=0

Hence, when x=0 we have:

y=4

Hence, the height was:

4 feet