Rate of Change from a Table

Front

What is the definition of rate of change?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity, often expressed as a ratio or a fraction.

Front

How do you calculate the rate of change from a table of values?

Back

To calculate the rate of change from a table, subtract the initial value from the final value and divide by the change in the independent variable.

Front

What is the formula for rate of change?

Back

Rate of Change = (Change in Dependent Variable) / (Change in Independent Variable) or (y2 - y1) / (x2 - x1).

Front

What does a positive rate of change indicate?

Back

A positive rate of change indicates that the dependent variable is increasing as the independent variable increases.

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that the dependent variable is decreasing as the independent variable increases.

Front

If the rate of change is zero, what does that mean?

Back

A rate of change of zero means that there is no change in the dependent variable as the independent variable changes.

Front

How can you interpret a rate of change of 6?

Back

A rate of change of 6 means that for every unit increase in the independent variable, the dependent variable increases by 6 units.

Front

What is the significance of units in rate of change?

Back

Units in rate of change provide context and meaning to the value, indicating how much one quantity changes in relation to another (e.g., dollars per day, gallons per minute).

Front

How do you find the average rate of change over an interval?

Back

The average rate of change over an interval is found by taking the difference in the values of the function at the endpoints of the interval and dividing by the difference in the input values.

Front

What is the relationship between rate of change and slope in a graph?

Back

The rate of change is equivalent to the slope of the line on a graph, representing the steepness and direction of the line.