Graphing Lines
Equations of the form ax + by = c where a, b, and c are real numbers are called linear equations in two variables and their graphs are straight lines.
In order to graph a linear equation, find the coordinates of two points on the line (i.e., solutions), and then plot the points and draw the line through the two points .
Examples
Example 1
Draw the graph of x + y = 6.
Solution 1
Select two values for x and find the corresponding y values:
Plot the points and draw a line through the two points (see Fig. 11-7 ).
Fig. 11-7.
Example 2
Draw the graph of 2x – y = 8.
Solution 2
Find the coordinates of two points on the line:
Plot the two points (1, -6) and (5, 2) and draw the line through these points (see Fig. 11-8 ).
Fig. 11-8.
Math Note: When graphing lines, it is best to select three points rather than two points in case an error has been made. If an error has been made, the three points will not line up.
Graphing Lines Practice Problems
Practice
Draw the graph of each of the following:
1. x – y = 3
2. –x + 4y = 9
3. 2x + 5y = 7
4. 3x – y = 6
5. –5x + y = 11
Answers
1. See Fig. 11-9
2. See Fig. 11-10
3. See Fig. 11-11
4. See Fig. 11-12
5. See Fig. 11-13
Fig. 11-9.
Fig. 11-10.
Fig. 11-11.
Fig. 11-12.
Fig. 11-13.
Practice problems for these concepts can be found at: Graphing Practice Test.
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