Find the linear model and use it to make a prediction.

Question

There are 2 leaves along 3 in. of an ivy vine. There are 14 leaves along 15 in. of the same vine. How many leaves are there along 6 in. of the vine?

Answer 1

The number of leaves depend on how long the vine is.  This is due to how much the vine can hold.

 

Let x = length of vine

Let y = number of leaves along the vine

 

 

First, we need to write this data in the form of points.

 

Point 1 = (3, 2)
Point 2 = (15, 14)

 

Since the model has to be linear, we know that we need to find the slope between these two point.

 

Slope = (14 - 2) / (15 - 3)

         = 12 / 12

          = 1

 

So far, the model is   y = x + b

 

Plug in the coordinate of the first point into this equation to find b.

 

 

2 = 3 + b

 

-1 = b

 

 

The model is

 

y = x - 1

 

 

Plug in x=6 into the model to find the number of leaves then the vine is 6 inches.