Rate of Change

Front

What is the rate of change?

Back

The rate of change is a measure of how a quantity changes in relation to another quantity, often expressed as a ratio of the change in the dependent variable (y) to the change in the independent variable (x).

Front

How do you calculate the rate of change?

Back

Rate of change can be calculated using the formula: Rate of Change = \frac{\Delta y}{\Delta x}, where \Delta y is the change in y and \Delta x is the change in x.

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 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 is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the rise (change in y) to the run (change in x).

Front

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

Back

The slope (m) can be found using the formula: m = \frac{y2 - y1}{x2 - x1}.

Front

What is the slope of the line through the points (3, 6) and (5, 6)?

Back

The slope is 0, indicating a horizontal line.

Front

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

Back

The slope is -\frac{5}{3}, indicating a downward slant.

Front

What does 'rise over run' mean in the context of slope?

Back

'Rise over run' refers to the vertical change (rise) divided by the horizontal change (run) between two points on a line.

Front

What is the formula for finding the rate of change in a real-world context?

Back

In a real-world context, the rate of change can be expressed as: Rate of Change = \frac{Change in Quantity}{Change in Time}.