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Study Guides > College Algebra

Introduction to Linear Functions

LEARNING OBJECTIVES

By the end of this lesson, you will be able to:
  • Represent a linear function.
  • Determine whether a linear function is increasing, decreasing, or constant.
  • Calculate and interpret slope.
  • Write the point-slope form of an equation.
  • Write and interpret a linear function.
Introduction to Linear Functions
An upward view of bamboo trees.A bamboo forest in China (credit: "JFXie"/Flickr)
Imagine placing a plant in the ground one day and finding that it has doubled its height just a few days later. Although it may seem incredible, this can happen with certain types of bamboo species. These members of the grass family are the fastest-growing plants in the world. One species of bamboo has been observed to grow nearly 1.5 inches every hour.[footnote]http://www.guinnessworldrecords.com/records-3000/fastest-growing-plant/[/footnote] In a twenty-four hour period, this bamboo plant grows about 36 inches, or an incredible 3 feet! A relation with a constant rate of change, such as the growth cycle of this bamboo plant, is a linear function. Recall from Functions and Function Notation that a function is a relation that assigns to every element in the domain exactly one element in the range. Linear functions are a specific type of function that can be used to model many real-world applications, such as plant growth over time. In this chapter, we will explore linear functions, their graphs, and how to relate them to data.  
Front view of a subway train, the maglev train. Shanghai MagLev Train (credit: "kanegen"/Flickr)

Like the growth of a bamboo plant, many situations involve a constant rate of change. Consider, for example, the first commercial maglev train in the world, the Shanghai MagLev Train. It carries passengers comfortably for a 30-kilometer trip from the airport to the subway station in only eight minutes.[footnote]http://www.chinahighlights.com/shanghai/transportation/maglev-train.htm[/footnote]

Suppose a maglev train were to travel a long distance, and that the train maintains a constant speed of 83 meters per second for a period of time once it is 250 meters from the station. How can we analyze the train’s distance from the station as a function of time? In this section, we will investigate a kind of function that is useful for this purpose, and use it to investigate real-world situations such as the train’s distance from the station at a given point in time.

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  • Precalculus. Provided by: OpenStax Authored by: Jay Abramson, et al.. Located at: https://openstax.org/books/precalculus/pages/1-introduction-to-functions. License: CC BY: Attribution. License terms: Download For Free at : http://cnx.org/contents/[email protected]..