Graphing Linear Functions | Mathematics

November 5, 2015 thetasctest

Graphing Linear Functions | Mathematics

In a recent blog post, we discussed the difference between linear and exponential functions. As you continue to prepare for the TASC Test Assessing Secondary Completion™ Mathematics subtest, it’s important you understand how to graph these functions.

Let’s start by taking a closer look at linear functions.


Interpreting Linear Graphs

Before we learn how to graph linear functions, we need to understand the data they represent.

Example 1: The graph below represents the price of a product versus the demand of a product. Can you explain this linear graph?  

Answer: Let’s pretend the product represented in the graph is gasoline. As the price of gasoline increases, the demand for gasoline decreases.

Example 2: The graph below represents the demand for land versus the population. Can you explain this linear graph?  

Answer: As the population increases, the demand for land increases.


How to Graph Linear Functions

Graphing linear relationships is a high emphasis topic on the TASC Mathematics subtest. The Khan Academy offers an example of how linear functions are graphed. Let’s take a look:

Problem: Agent Hunt transferred classified files from the CIA mainframe onto his flash drive. The flash drive already had 60 megabytes on it before the transfer, and an additional 4 megabytes were transferred onto it each second. Graph the size of the files on Agent Hunt's drive (in megabytes) as a function of time (in seconds).

Let’s break this problem down:

  • Before the transfer, the flash drive had 60 megabytes on it.
  • When the time is 0, the file size is 60 megabytes.
  • The graph of the function should pass through the point (0, 60).
  • When the time increases by 1 second, the file size increases by 4 megabytes.

Do you see a linear relationship in the data forming? Let’s keep going and solve another point on the linear graph:

  • To help see the slope of the linear line better, let’s increase the time by 10. The file size then increases to 10⋅4=40.
  • The graph of the function should pass through point (0+10, 60+40), which is the point (10, 100).

Now that we understand the linear relationship, we can graph the linear function: 

Graph image via Khan Academy.


Stay tuned for the next TASC Mathematics subtest post where we will learn how to graph exponential functions.

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