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 represented as the slope of a line on a graph.

Front

How do you calculate the rate of change between two points (x1, y1) and (x2, y2)?

Back

The rate of change (slope) is calculated using the formula: (y2 - y1) / (x2 - x1).

Front

What does a rate of change of 0 indicate about a function?

Back

A rate of change of 0 indicates that the function is constant; there is no change in the y-value as the x-value changes.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If the rate of change is positive, what does that indicate about the relationship between the variables?

Back

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

Front

If the rate of change is negative, what does that indicate about the relationship between the variables?

Back

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

Front

What is the relationship between rate of change and slope?

Back

The rate of change is equivalent to the slope of a line, representing the steepness and direction of the line.

Front

How can you interpret a slope of 2 in a real-world context?

Back

A slope of 2 means that for every 1 unit increase in the x-variable, the y-variable increases by 2 units.

Front

What is the significance of units in rate of change?

Back

Units in rate of change provide context for the relationship between the variables, indicating how much one variable changes in relation to another.