Rate of Change

Front

What is the 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 slope.

Front

How do you calculate the rate of change between two points on a graph?

Back

Rate of change = (Change in y) / (Change in x) = (y2 - y1) / (x2 - x1)

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that the quantity is decreasing over time.

Front

What does a positive rate of change indicate?

Back

A positive rate of change indicates that the quantity is increasing over time.

Front

What is the slope of a line?

Back

The slope of a line is the rate of change of the y-coordinate with respect to the x-coordinate, often represented as 'm' in the equation y = mx + b.

Front

If a line has a slope of -3, what does this mean in terms of rate of change?

Back

It means that for every 1 unit increase in x, the value of y decreases by 3 units.

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

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

Back

The rate of change can be interpreted as the steepness of the graph; steeper lines indicate a greater rate of change.

Front

What does a horizontal line on a graph represent in terms of rate of change?

Back

A horizontal line represents a rate of change of 0, indicating that the quantity does not change.

Front

What is a real-world example of rate of change?

Back

An example is the speed of a car, which is the rate of change of distance with respect to time.