Rate of Change

Front

What is the definition of rate of change?

Back

The rate of change is a measure of how a quantity changes in relation to another quantity, often expressed as a ratio or fraction.

Front

How is the rate of change calculated from a graph?

Back

The rate of change can be calculated by finding the slope of the line on the graph, which is the change in the y-values divided by the change in the x-values.

Front

What does a positive rate of change indicate?

Back

A positive rate of change indicates that as one quantity increases, the other quantity also increases.

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that as one quantity increases, the other quantity decreases.

Front

What is the formula for calculating the slope of a line?

Back

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

Front

What is the rate of change for a horizontal line?

Back

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

Front

What is the rate of change for a vertical line?

Back

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

Front

How can you interpret a rate of change of 1?

Back

A rate of change of 1 means that for every unit increase in the x-value, the y-value also increases by 1 unit.

Front

What does a rate of change of -1/3 represent in a real-world context?

Back

A rate of change of -1/3 means that for every 3 units increase in the x-value, the y-value decreases by 1 unit.

Front

What is the significance of a steep slope in terms of rate of change?

Back

A steep slope indicates a greater rate of change, meaning that the dependent variable changes significantly with a small change in the independent variable.