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 the relationship between rate of change and slope?

Back

Rate of change is the same as slope; both represent the ratio of the change in the vertical direction (y) to the change in the horizontal direction (x).

Front

How do you calculate the rate of change?

Back

Rate of change can be calculated using the formula: (change in y) / (change in x), also known as rise over run.

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 formula for slope?

Back

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

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no change in the y-value as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x is 0, leading to division by zero.

Front

What does 'rise over run' mean?

Back

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

Front

If a line has a slope of 3, what does this mean?

Back

A slope of 3 means that for every 1 unit increase in x, the value of y increases by 3 units.