Question

The rate at which trees grow over time can be represented with a linear model. The tables provided show the heights of five different trees over a ten-year time span.

"Which tables show a linear relationship between years and height? Select THREE that apply.

Answer 1

The table that represents a linear relationship is (c)

Identifying the table that represents a linear relationship

From the question, we have the following parameters that can be used in our computation:

The table of values

By definition:

A table that represents a linear relationship is a table that has a constant rate of change i.e. slope

This means that if represented on a graph, a line must start all the points on the graph

The slope is calculated using

Slope = Change in y/Change in x

Using the above as a guide, we have the following:

Table (b)

Rate = (25.4 - 22.7)/(1 - 0)

Rate = 2.7

Using another point, we have

Rate = (31.9 - 25.4)/(3 - 1)

Rate = (40.00 - 31.9)/(5 - 3) = 3.25

3.25 and 2.7 are not the same

So, table b is not a linear model

Table (c)

Rate = (8.4 - 6.2)/(1 - 0)

Rate = 2.2

Using another point, we have

Rate = (10.6 - 8.4)/(2 - 1)

Rate = 2.2

Using another point, we have

Rate = (15.0 - 10.6)/(4 - 2)

Rate = 2.2

Using another point, we have

Rate = (21.6 - 15.0)/(7 - 4)

Rate = 2.2

Using another point, we have

Rate = (28.2 - 21.6)/(10 - 7)

Rate = 2.2

Hence, the table that represents a linear relationship is (c)