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## Graphing Linear Equations in Two-VariablesBuild a table of ordered pairs where the x-values are in a sequence and the y-values are in a sequence. When you plot these points (ordered pairs) you will see that they form a straight line. Always choose 1. Given 2x − 3y = 6 build the table for using an arithmetic sequence as replacement values. Note: In this equation if you choose consecutive integers for x you will find some y-values that are fractions. By noting that the constant 6 is a multiple of 3 and the coefficient of y is 3, you can choose your sequence for the x-values to be multiples of 3 . Now, when you are solving for the y-values and divide by the coefficient-3 you will obtain a sequence of integers for the y-values.
Check to see that both columns of values are arithmetic sequences.
The following is another approach to graphing this equation.
If
Now you must CHECK the top and bottom points in the table to be sure that they are points on the line: For the point (- 3, - 4) replace x = - 3 and y = - 4 in the given equation 2x − 3y = 6 CHECK: For the point (9, 4) replace x = 9 and y = 4 in the given equation 2x − 3y = 6 CHECK: |