Average Rate of Change NYS Regents Practice

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

How do you calculate the slope of a line?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

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

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 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 changes.

Front

If a line passes through the points (1, 2) and (3, 6), what is the slope?

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).

Front

What is the average rate of change between the points (2, 4) and (6, 12)?

Back

The average rate of change is 2, calculated as (12 - 4) / (6 - 2).

Front

What is the formula for finding the average rate of change?

Back

The formula is Average Rate of Change = (f(b) - f(a)) / (b - a), where a and b are the interval endpoints.

Front

What does a slope of 4/5 represent?

Back

A slope of 4/5 means that for every 5 units you move horizontally to the right, the line rises 4 units vertically.