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 expressed as the change in the dependent variable divided by the change in the independent variable.

Front

How do you calculate the slope of a line?

Back

The slope (m) of a line is calculated using the formula: m = (change in y) / (change in x) or m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship between the two variables.

Front

What is the formula for finding the rate of change between two points?

Back

The rate of change between two points (x1, y1) and (x2, y2) is given by: Rate of Change = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line that passes through the points (3, 4) and (7, 8)?

Back

The slope is m = (8 - 4) / (7 - 3) = 4 / 4 = 1.

Front

What is the rate of change of Mrs. Gordon's distance if she travels 5 feet in 2 seconds?

Back

The rate of change is 5 feet / 2 seconds = 2.5 feet per second.

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, which is the definition of slope.

Front

If the coordinates of two points are (1, 2) and (4, 5), what is the rate of change?

Back

Rate of Change = (5 - 2) / (4 - 1) = 3 / 3 = 1.

Front

What is the significance of an undefined slope?

Back

An undefined slope occurs when the line is vertical, meaning there is no change in x (the denominator is zero), and thus the rate of change cannot be calculated.