Constant Rate of Change

Front

What is a constant rate of change?

Back

A constant rate of change refers to a situation where a quantity changes at a consistent rate over time, meaning the change in one variable is proportional to the change in another variable.

Front

How do you identify a constant rate of change from a table of values?

Back

To identify a constant rate of change from a table, calculate the difference in the dependent variable divided by the difference in the independent variable for each pair of values. If the result is the same for all pairs, there is a constant rate of change.

Front

What is the formula for calculating the rate of change?

Back

The formula for calculating the rate of change is: Rate of Change = (Change in y) / (Change in x).

Front

In the context of a graph, what does a straight line indicate about the rate of change?

Back

A straight line on a graph indicates a constant rate of change, meaning that the relationship between the two variables is linear.

Front

What does a slope of 0 indicate in a rate of change scenario?

Back

A slope of 0 indicates that there is no change in the dependent variable as the independent variable changes, meaning the rate of change is constant at zero.

Front

How can you determine the constant rate of change from a graph?

Back

To determine the constant rate of change from a graph, calculate the slope of the line by selecting two points on the line and using the formula: (y2 - y1) / (x2 - x1).

Front

What is the significance of the y-intercept in a linear equation related to constant rate of change?

Back

The y-intercept represents the value of the dependent variable when the independent variable is zero, providing a starting point for the linear relationship.

Front

How does the concept of constant rate of change apply to real-world scenarios?

Back

Constant rate of change applies to various real-world scenarios, such as calculating speed, cost per item, or any situation where one quantity consistently changes in relation to another.

Front

What is an example of a constant rate of change in a real-life situation?

Back

An example of a constant rate of change is a car traveling at a steady speed of 60 miles per hour; for every hour, the car covers 60 miles.

Front

What is the relationship between constant rate of change and linear functions?

Back

Constant rate of change is a defining characteristic of linear functions, where the graph is a straight line and the rate of change remains the same throughout.