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 a ratio or slope.

Front

How do you calculate the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

In the equation y = mx + b, what does 'b' represent?

Back

The 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

What is the slope of the line that passes through the points (2, 4) and (6, 12)?

Back

The slope is 2.

Front

How do you interpret a negative slope?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Front

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

Back

The formula is Rate of Change = (Change in y) / (Change in x) = (y2 - y1) / (x2 - x1).

Front

What does 'm' represent in the slope-intercept form of a linear equation?

Back

The 'm' represents the slope of the line.

Front

If the rate of change is -3/2, what does this indicate about the relationship between the variables?

Back

It indicates that for every 2 units increase in the independent variable, the dependent variable decreases by 3 units.

Front

What is the significance of a slope of zero?

Back

A slope of zero indicates a horizontal line, meaning there is no change in the dependent variable as the independent variable changes.