Rate of Change

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the constant amount that y changes for every unit change in x, often represented as the slope of the line.

Front

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

Back

To calculate the rate of change, take the difference in the y-values and divide it by the difference in the x-values between two points.

Front

What does a negative rate of change indicate?

Back

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

Front

What is the formula for slope (rate of change)?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

If the slope of a line is 3, what does this mean?

Back

A slope of 3 means that for every 1 unit increase in x, y increases by 3 units.

Front

What is the significance of a slope of zero?

Back

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

Front

What does an undefined slope represent?

Back

An undefined slope represents a vertical line, where x does not change but y can take any value.

Front

How can you interpret the rate of change in a real-world context?

Back

The rate of change can represent speed, cost per item, or any other quantity that changes in relation to another.

Front

What is the average rate of change?

Back

The average rate of change is the total change in y divided by the total change in x over a specified interval.

Front

How do you find the average rate of change from a graph?

Back

To find the average rate of change from a graph, identify two points on the line, and use the slope formula.