Question

does the table of values represent a function that is linear or nonlinear? select from the drop-down menus to correctly complete the statement. for each pair of points, the rate of change is choose... since the rate of change choose..., the function is choose...

Explanation:

Step1: Calculate rate of change between (1,4) and (3,10)

The formula for rate of change (slope) is $\frac{y_2 - y_1}{x_2 - x_1}$. So, $\frac{10 - 4}{3 - 1} = \frac{6}{2} = 3$.

Step2: Calculate rate of change between (3,10) and (7,22)

Using the slope formula: $\frac{22 - 10}{7 - 3} = \frac{12}{4} = 3$.

Step3: Calculate rate of change between (7,22) and (9,28)

Using the slope formula: $\frac{28 - 22}{9 - 7} = \frac{6}{2} = 3$.

Step4: Analyze the rate of change

Since the rate of change is 3 for each pair of points, it is constant. A function with a constant rate of change is linear.

Answer:

For each pair of points, the rate of change is 3. Since the rate of change is constant, the function is linear.