Rate of Change

Front

What is the definition of rate of change?

Back

The rate of change is a measure of how a quantity changes in relation to another quantity, often expressed as the change in the dependent variable divided by the change in the independent variable.

Front

How do you calculate the rate of change?

Back

Rate of change = (Change in y) / (Change in x) or (Rise) / (Run).

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that as one quantity increases, the other quantity decreases.

Front

What is the average rate of change?

Back

The average rate of change is the total change in a quantity divided by the total time over which the change occurred.

Front

If a function is linear, what can be said about its rate of change?

Back

If a function is linear, its rate of change is constant.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

What does it mean if the rate of change is not constant?

Back

If the rate of change is not constant, the relationship between the variables is non-linear, meaning the slope varies at different points.

Front

How can you find the rate of change from a graph?

Back

To find the rate of change from a graph, select two points on the line, determine the rise and run between them, and calculate the slope.

Front

What is the formula for average rate of change between two points (x1, y1) and (x2, y2)?

Back

Average rate of change = (y2 - y1) / (x2 - x1).

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent various real-world rates, such as speed, growth rate, or efficiency, depending on the context of the variables.