Rate of Change

Front

What is the rate of change?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity. It is often represented as the slope of a line in a graph.

Front

What is slope in the context of a graph?

Back

Slope is a measure of the steepness of a line, calculated as the change in y (rise) divided by the change in x (run).

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

Slope = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the slope of the line that passes through the points (4, 5) and (4, 9)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

What is the slope of the line that passes through the points (0, 0) and (5, 5)?

Back

Slope = (5 - 0) / (5 - 0) = 5 / 5 = 1.

Front

What is the formula for finding the rate of change?

Back

Rate of Change = (Change in y) / (Change in x).

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates a horizontal line, meaning that y does not change as x changes.