Question

Determine whether the information in each table is linear. If so find the constant rate of change. If not explain your reasoning..

Answer 1

EXPLANATION

Since we have the table with the values of x and y, we can draw the graph as show as follows:

The rate of change can be computed by taking two given points and calculating the slope as shown as follows:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

As we have (x_1,y_1) = (1,13) and (x_2,y_2) = (3,39), substituting terms:

$\text{Slope}=\frac{39-13}{3-1}$

Subtracting numbers:

$Slope=\frac{26}{2}$

Simplifying:

$\text{Slope}=rate_{\text{ }}of_{\text{ }}change=13$

The constant rate of change is 13

The function is linear because we have a constant rate of change and the form of the graph is a line.