Question

Determine the correct answer about whether a Table of Values represents a Linear Function. Х 1 1 2 3 4 у 5 10 15 20 Table of Values represents a Constant Rate of Change x-values have a Constant Rate of Change y-values have a Constant Rate of Change Plot points on a Graph and see

Answer 1

Answer

Table of values represents a constant rate of change

Explanations:

From the table:

The values of x are 1 , 2 , 3 , 4 , 5.

The corresponding values of y are 5, 10, 15, 20

For a linear function, there must be a constant rate of change:

That is, △y / △x should be constant

`\begin{gathered} x_1=1,x_2=2,y_1=5,y_2=\text{ 10} \\ (\triangle y)/(\triangle x)=\text{ }(y_2-y_1)/(x_2-x_1) \\ (\triangle y)/(\triangle x)=\text{ }(10-5)/(2-1) \\ (△y)/(△x)=\text{ 5} \end{gathered}`

Also considering:

`\begin{gathered} x_3=3,x_4=4,y_3=15,y_4=20 \\ (\triangle y)/(\triangle x)=\text{ }(y_4-y_3)/(x_4-x_3) \\ (\triangle y)/(\triangle x)=\text{ }(20-15)/(4-3) \\ (\triangle y)/(\triangle x)=(5)/(1) \\ (\triangle y)/(\triangle x)=\text{ 5} \end{gathered}`

In all the points considered, the rate of change is the same. This means that the table of values represent a constant rate of change, it therefore represents a linear function.