Rate of Change and Slope

Front

What is the rate of change?

Back

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

Front

How do you calculate the slope of a line?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as one variable increases, the other variable also increases.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating no change in the y-value as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning the x-value does not change while the y-value does.

Front

Find the slope of the line that passes through (1, 2) and (3, 6).

Back

The slope is 2.

Front

Find the slope of the line that passes through (4, 5) and (4, 9).

Back

The slope is undefined.

Front

If the rate of change is -3, what does this imply?

Back

This implies that for every unit increase in the independent variable, the dependent variable decreases by 3 units.

Front

What is the relationship between slope and rate of change?

Back

The slope of a line represents the rate of change between the two variables represented on the axes.