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. It is often expressed as a fraction or ratio.

Front

How do you calculate the rate of change between two points (x1, y1) and (x2, y2)?

Back

Rate of Change = (y2 - y1) / (x2 - x1)

Front

What does a rate of change of 0 indicate about two points?

Back

A rate of change of 0 indicates that the y-values are the same for different x-values, meaning there is no change in the vertical direction.

Front

What does an undefined rate of change indicate?

Back

An undefined rate of change occurs when the x-values are the same (x1 = x2), indicating a vertical line where the change in x is zero.

Front

Calculate the rate of change between the points (2, 5) and (4, 9).

Back

Rate of Change = (9 - 5) / (4 - 2) = 4 / 2 = 2.

Front

Calculate the rate of change between the points (1, 2) and (1, 5).

Back

Rate of Change is undefined because the x-values are the same.

Front

If the points are (3, -1) and (7, 3), what is the rate of change?

Back

Rate of Change = (3 - (-1)) / (7 - 3) = 4 / 4 = 1.

Front

What is the significance of a positive rate of change?

Back

A positive rate of change indicates that as the x-value increases, the y-value also increases.

Front

What is the significance of a negative rate of change?

Back

A negative rate of change indicates that as the x-value increases, the y-value decreases.

Front

Find the rate of change between the points (-2, 4) and (2, 8).

Back

Rate of Change = (8 - 4) / (2 - (-2)) = 4 / 4 = 1.