Constant Rate of Change Graphs

Front

What is a constant rate of change?

Back

A constant rate of change refers to a situation where the change in one quantity is consistent with the change in another quantity over time, often represented as a linear relationship in a graph.

Front

How can you identify a constant rate of change on a graph?

Back

A constant rate of change can be identified on a graph by a straight line, where the slope of the line remains the same throughout.

Front

What does the slope of a line represent in the context of constant rate of change?

Back

The slope of a line represents the rate of change between the two variables plotted on the graph, indicating how much one variable changes for a unit change in the other variable.

Front

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

Back

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

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of the dependent variable when the independent variable is zero.

Front

How do you write the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the difference between positive and negative slopes?

Back

A positive slope indicates that as one variable increases, the other variable also increases, while a negative slope indicates that as one variable increases, the other variable decreases.

Front

How can you determine the rate of change from a table of values?

Back

To determine the rate of change from a table of values, calculate the difference in the dependent variable divided by the difference in the independent variable for two points.

Front

What is a real-world example of a constant rate of change?

Back

A real-world example of a constant rate of change is a car traveling at a steady speed, where the distance traveled increases consistently over time.

Front

What role does a graph play in understanding constant rates of change?

Back

A graph visually represents the relationship between two variables, making it easier to identify trends, rates of change, and the nature of the relationship.