Rate of Change

Front

What is the definition of rate of change?

Back

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

Front

How do you calculate the rate of change between two points on a graph?

Back

The rate of change is calculated by taking the difference in the y-values and dividing it by the difference in the x-values (slope formula: (y2 - y1) / (x2 - x1)).

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

In the context of a business, what does a higher rate of change signify?

Back

A higher rate of change in a business context often signifies faster growth or decline in sales, revenue, or other key performance indicators.

Front

What is the significance of the slope in a linear equation?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

How can the rate of change be represented in a real-world scenario?

Back

The rate of change can be represented in various scenarios, such as speed (distance over time), cost per item, or growth rates in finance.

Front

What is the formula for calculating the average rate of change over an interval?

Back

The average rate of change over an interval [a, b] is given by (f(b) - f(a)) / (b - a).

Front

What is the relationship between rate of change and derivatives in calculus?

Back

In calculus, the derivative of a function at a point represents the instantaneous rate of change of the function at that point.

Front

How does the rate of change apply to a linear function?

Back

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