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 or another variable. It is often represented as a slope in a graph.

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 the independent variable.

Front

What is the formula for slope?

Back

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

Front

If a climber's altitude changes from 400 feet to 700 feet over 4 hours, what is the average rate of change?

Back

The average rate of change is 75 feet per hour.

Front

What does a positive slope indicate about a graph?

Back

A positive slope indicates that as the independent variable increases, the dependent variable also increases.

Front

What does a negative slope indicate about a graph?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Front

What is the significance of a slope of zero?

Back

A slope of zero indicates that there is no change in the dependent variable as the independent variable changes; the graph is horizontal.

Front

How do you interpret a slope of -4/3?

Back

A slope of -4/3 means that for every 3 units increase in the x-direction, the y-value decreases by 4 units.

Front

What is the average rate of change of Pete's height from 3 to 5 years if he grows 8 inches?

Back

The average rate of change is 4 inches per year.

Front

How do you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, determine their coordinates, and apply the slope formula: m = (y2 - y1) / (x2 - x1).