Algebra by Denise Szecsei

Author:Denise Szecsei
Language: eng
Format: epub
Publisher: Career Press
Published: 2011-08-11T16:00:00+00:00

Figure 6.1: The graph of f(x) = 3x + 2.

Once you have determined some of the ordered pairs that are generated by the function, I recommend graphing them. A carefully drawn picture or a graph can give lots of insight into the nature of the function. The graph of these ordered pairs is shown in Figure 6.1 on page 122.

Now that we have a picture of this function we can make some observations. First of all, notice that all of the points appear to lie on the same line. This function was called a linear function, and now that makes sense. Linear functions with one independent variable and one dependent variable have graphs that look like lines.

The graph of f(x) = 3x + 2. is a line that is not horizontal like the x-axis, nor is it vertical like the y-axis. It is worth measuring the slant, or slope, of lines that are not vertical or horizontal. The slope of a line is defined as the ratio of the “rise” of a graph divided by the “run” of the graph, or the “rise over the run” of the graph. The rise of the graph is a measurement of the change in the dependent variable (the variable y), and the run of the graph is a measurement of the change in the independent variable (the variable x):

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