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

$\begin{gathered} x_1=1,x_2=2,y_1=5,y_2=\text{ 10} \\ \frac{\triangle y}{\triangle x}=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ \frac{\triangle y}{\triangle x}=\text{ }\frac{10-5}{2-1} \\ \frac{△y}{△x}=\text{ 5} \end{gathered}$

Also considering:

$\begin{gathered} x_3=3,x_4=4,y_3=15,y_4=20 \\ \frac{\triangle y}{\triangle x}=\text{ }\frac{y_4-y_3}{x_4-x_3} \\ \frac{\triangle y}{\triangle x}=\text{ }\frac{20-15}{4-3} \\ \frac{\triangle y}{\triangle x}=\frac{5}{1} \\ \frac{\triangle y}{\triangle x}=\text{ 5} \end{gathered}$

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.