3.1 Rate of Change and Slope

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

What does 'slope' represent in a linear function?

Back

The slope represents the rate of change of the function, indicating how much the dependent variable changes for a unit change in the independent variable.

Front

How do you determine if a function is linear?

Back

A function is linear if it can be represented by a straight line on a graph, meaning it has a constant rate of change.

Front

What is the formula for calculating slope?

Back

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

Front

If a function has a slope of 6, what does this indicate?

Back

A slope of 6 indicates that for every 1 unit increase in the x-value, the y-value increases by 6 units.

Front

What is the slope of the line represented by the points (2, 3) and (4, 6)?

Back

The slope is (6 - 3) / (4 - 2) = 3 / 2.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions have varying rates of change and graph as curves.

Front

How can you tell if a table of values represents a linear function?

Back

If the differences between consecutive y-values divided by the differences between consecutive x-values are constant, the function is linear.

Front

What does a negative slope indicate about a function?

Back

A negative slope indicates that as the x-value increases, the y-value decreases.

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.