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 (x1, y1) and (x2, y2)?

Back

Rate of change = (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

What is the rate of change for a linear function?

Back

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

Front

If a line has a slope of 2, what is the rate of change?

Back

The rate of change is 2, meaning for every 1 unit increase in x, y increases by 2 units.

Front

What is the rate of change if the slope of a line is -3?

Back

The rate of change is -3, meaning for every 1 unit increase in x, y decreases by 3 units.

Front

What does a slope of 0 indicate about the rate of change?

Back

A slope of 0 indicates that there is no change in y as x changes; the line is horizontal.

Front

What is the significance of the y-intercept in relation to rate of change?

Back

The y-intercept is the value of y when x is 0; it does not affect the rate of change but indicates where the line crosses the y-axis.

Front

How can you determine which of two lines has a greater rate of change?

Back

Compare the slopes of the lines; the line with the steeper slope has a greater rate of change.