Rate of Change

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?

Back

Rate of change = (Change in value) / (Change in time) or (y2 - y1) / (x2 - x1).

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 does a negative rate of change indicate?

Back

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

Front

If a car travels 60 miles in 1 hour, what is the rate of change of distance with respect to time?

Back

The rate of change is 60 miles per hour.

Front

What is the rate of change in the context of a graph?

Back

The rate of change in a graph is represented by the slope of the line, which indicates how steep the line is.

Front

If a line has a slope of 2, what does this mean in terms of rate of change?

Back

It means that for every 1 unit increase in x, y increases by 2 units.

Front

What is the rate of change if a plant grows 3 cm in 2 weeks?

Back

Rate of change = 3 cm / 2 weeks = 1.5 cm per week.

Front

How can you interpret a rate of change of 0?

Back

A rate of change of 0 indicates that there is no change in the quantity over time.

Front

What is the formula for calculating average rate of change?

Back

Average rate of change = (f(b) - f(a)) / (b - a) for a function f between points a and b.