Comparing Linear Functions

Front

What is a linear function?

Back

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of one variable with respect to another. It indicates how much the dependent variable changes for a unit change in the independent variable.

Front

How do you determine if a function is linear or nonlinear?

Back

A function is linear if it can be represented by a straight line on a graph. If the graph is curved or does not form a straight line, the function is nonlinear.

Front

What is the formula for calculating the slope between two points?

Back

Front

What is the y-intercept of a linear function?

Back

Front

What does it mean if a slope is negative?

Back

A negative slope indicates that as one variable increases, the other variable decreases. This shows an inverse relationship between the two variables.

Front

What is the difference between a constant rate of change and a variable rate of change?

Back

A constant rate of change means the relationship between variables is linear, while a variable rate of change indicates a nonlinear relationship where the rate of change varies.

Front

How can you identify the rate of change from a table of values?

Back

To identify the rate of change from a table, calculate the difference in the dependent variable divided by the difference in the independent variable for consecutive pairs of values.

Front

What is a real-world example of a linear function?

Back

An example of a linear function is calculating the total cost of items where each item has a fixed price. The total cost increases linearly with the number of items purchased.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect, meaning they have a constant rate of change.