Question

A) Explain how you would use this table of values to determine if it represents a linear or a non-linear relationship.

a) Linear relationships have a constant rate of change; non-linear relationships do not.
b) Linear relationships always pass through the origin; non-linear relationships do not.
c) Linear relationships have exponential growth; non-linear relationships have exponential decay.
d) Linear relationships have decreasing values; non-linear relationships have increasing values.

Answer 1

To determine if a table of values represents a linear or non-linear relationship, you can use criteria such as constant rate of change, passing through the origin, exponential growth or decay, and increasing or decreasing values.

Step-by-step explanation:

To determine if a table of values represents a linear or non-linear relationship, you can use the following criteria:

1. Constant rate of change: Linear relationships have a constant rate of change, meaning that the change in the dependent variable for every unit change in the independent variable remains the same. Non-linear relationships do not have a constant rate of change.
2. Passing through the origin: Linear relationships always pass through the origin (0,0). Non-linear relationships may or may not pass through the origin.
3. Exponential growth and decay: Linear relationships do not have exponential growth or decay. Non-linear relationships can have exponential growth or decay.
4. Increasing or decreasing values: Linear relationships can have both increasing and decreasing values. Non-linear relationships can also have both increasing and decreasing values.

By analyzing the table of values and checking if these criteria are met, you can determine whether the relationship is linear or non-linear.