Average Rate of Change

Front

What is the Average Rate of Change (ARC)?

Back

The Average Rate of Change (ARC) is a measure of how much a quantity changes on average over a specific interval. It is calculated using the formula: ARC = (y2 - y1) / (x2 - x1).

Front

How do you calculate the slope of a line?

Back

The slope of a line is calculated using the formula: slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no change in the y-value as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the x-value does not change while the y-value does.

Front

How do you find the average rate of change of a function between two points?

Back

To find the average rate of change, use the formula: ARC = (f(x2) - f(x1)) / (x2 - x1) for the function f.

Front

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

Back

The slope can represent rates of change, such as speed, growth, or decline in various real-world scenarios.

Front

If Pete's height increased from 40 inches to 48 inches between ages 3 and 5, what is the average rate of change?

Back

The average rate of change is (48 - 40) / (5 - 3) = 8 / 2 = 4 inches per year.