Slope Flashcard Review

Front

What is the average rate of change?

Back

The average rate of change is the change in the value of a quantity divided by the change in time. It represents how much a quantity changes on average over a specific interval.

Front

How do you calculate the average rate of change from a table of values?

Back

To calculate the average rate of change from a table, subtract the initial value from the final value and divide by the change in time.

Front

What is the formula for slope?

Back

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

Front

What does a slope of 1 indicate?

Back

A slope of 1 indicates that for every unit increase in x, y increases by the same amount, resulting in a 45-degree angle line.

Front

What does a slope of 0 indicate?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where x does not change as y changes.

Front

How do you find the slope between two points?

Back

To find the slope between two points, use the formula m = (y2 - y1) / (x2 - x1) with the coordinates of the two points.

Front

What is the average rate of change of altitude for a climber who goes from 400 feet to 700 feet in 4 hours?

Back

The average rate of change is (700 - 400) / (6 - 2) = 300 / 4 = 75 feet per hour.

Front

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

Back

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

Front

What is the average rate of change in snowfall from January 8 to January 11 if the inches of snowfall are 4 and 6 respectively?

Back

The average rate of change is (6 - 4) / (11 - 8) = 2 / 3 = 2/3 inches per day.