Making a Table of Values

The relation between the variables of an equation can be shown by making a table of values. This is helpful when graphing any equation, not only linear ones. The following linear equation will be drawn as an example. 6x-3y=- 12 There are four steps to making a table of values for an equation.

Isolate One Variable

If in the given equation none of the variables are isolated on one side, it is convenient to do so before making the table of values. This will simplify the rest of the process. A variable can be isolated using the Properties of Equality. If the variables presented in the equation are x and y, usually the latter one will be isolated.

6x-3y=- 12

SubEqn

LHS-6x=RHS-6x

- 3y=- 6x-12

DivEqn

.LHS /(- 3).=.RHS /(- 3).

y=- 6x-12/- 3

▼

Simplify right-hand side

WriteSumFrac

Write as a sum of fractions

y=- 6x/- 3+- 12/- 3

DivNegNeg

- a/- b=a/b

y=6x/3+12/3

CalcQuot

Calculate quotient

y=2x+4

Often the non-isolated variable is called the input and the isolated variable is called the output.

Choose the Values for the Non-Isolated Variable(s)

A table of values will usually have as many columns as there are variables plus one. In this case, the first column is for the values of the input. The second column is for substituting values from the first column into the rewritten equation. The third column shows the values of the output corresponding to its input.

x	2x+4	y=2x+4

Next, the values of the non-isolated input variable x should be chosen. It can be done arbitrarily. However, the values should always belong to the domain of the function represented by the given equation. Recall that the domain of a linear function are all real numbers. In this case - 2, 0, 0.5, and 1 will be used.

x	2x+4	y=2x+4
- 2
0
0.5
1

For quadratic equations it is useful to choose input values that lie on both sides of the axis of symmetry, especially if the table will be used for graphing the equation.

Substitute the Values Into the Rewritten Equation

In this step the input values will be substituted into the rewritten equation where the output variable is isolated on the left-hand side.

x	2x+4	y=2x+4
- 2	2( - 2)+4
0	2( 0)+4
0.5	2( 0.5)+4
1	2( 1)+4

Calculate the Values of the Isolated Variable

The last step is to simplify the expressions in the second column and write the result in the the last column. These are the outputs corresponding to the input from each row.

x	2x+4	y=2x+4
- 2	2( - 2)+4	0
0	2( 0)+4	4
0.5	2( 0.5)+4	5
1	2( 1)+4	6

If the expressions in the second column are too complicated to calculate mentally, extra columns where the partial results are written can be added as needed. However, the last column should always be the outputs.

x	2x+4	Simplify	y=2x+4
- 2	2( - 2)+4	- 4+4	0
0	2( 0)+4	0+4	4
0.5	2( 0.5)+4	1+4	5
1	2( 1)+4	2+4	6

The table of values can be reduced to a table with only two columns — one with inputs and one with outputs. Note that for the output column we write only the variable.

6x-3y=- 12
x	y
- 2	0
0	4
0.5	5
1	6

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