rate of change

Front

What is the rate of change?

Back

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

Front

How do you calculate the rate of change?

Back

Rate of change can be calculated using the formula: Rate of Change = \( \frac{\text{Change in Value}}{\text{Change in Time}} \) or \( \frac{y_2 - y_1}{x_2 - x_1} \) for two points (x1, y1) and (x2, y2).

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 a constant rate of change?

Back

A constant rate of change means that the change in one quantity is consistent over time, resulting in a straight line when graphed.

Front

What is the rate of change of a linear function?

Back

The rate of change of a linear function is constant and is represented by the slope of the line.

Front

If a car travels 60 miles in 1 hour, what is the rate of change?

Back

The rate of change is 60 miles per hour.

Front

What is the slope in the context of rate of change?

Back

The slope is a measure of the steepness of a line and represents the rate of change between two variables.

Front

How can you represent rate of change graphically?

Back

Rate of change can be represented graphically as the slope of a line on a graph, where the x-axis represents one variable and the y-axis represents another.

Front

What is the significance of the y-intercept in a rate of change context?

Back

The y-intercept represents the initial value of the dependent variable when the independent variable is zero.