Recognizing a Linear Relationship

In this lesson, you will learn how to recognize a linear relationship in various forms, including tabular data, Cartesian plots, and English descriptions. One way to identify a linear function in a table is to look for a constant difference in outputs when the inputs vary by one. In a Cartesian graph, the constant rate of change can be found by calculating the change in output over the change in input. Finally, you can identify a linear relationship in English descriptions by looking for words like "per" or "fixed cost," which indicate a constant rate of change or initial value, respectively.

Recognize a linear relationship in whatever way it may be presented (tabular data, Cartesian plot, English).

• How can you recognize a linear relationship from a table?
• What is the difference between an arithmetic and geometric relationships?
• What is true about the values in a table of a linear relationship?
• How do you write a linear function from values in a table?
• How do you compute the slope or constant rate of a line from a graph?
• What does marginal cost mean in a business relationship?
• How can you write a linear function from a real-world business relationship in words?