Ideas
Substitution
A table of values is one way to display a linear relationship between x and y values. A linear equation can be used to generate y values from given x values. Therefore, a table of values can then be created to display multiple (x,y) solutions for a given linear relation.
Construct a table of values using the following equation:y=3x-5
The table of values for this equation connects the y-values that result from substituting in a variety of x-values. Let's complete the table of values below:
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y |
To substitute x=1 into the equation y=3x-5, replace all accounts of x with 1.
| \displaystyle y | \displaystyle = | \displaystyle 3 \times 1-5 |
| \displaystyle = | \displaystyle 3-5 | |
| \displaystyle = | \displaystyle -2 |
So then -2 must go in the first entry in the row of y-values.
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | -2 |
Next let's substitute x=2 into the equation y=3x-5.
For x=2:
| \displaystyle y | \displaystyle = | \displaystyle 3 \times 2-5 |
| \displaystyle = | \displaystyle 6-5 | |
| \displaystyle = | \displaystyle 1 |
So then 1 must go in the second entry in the row of y-values.
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | -2 | 1 |
Continue with this process of substituting the remaining values of y to complete the table of values:
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | -2 | 1 | 4 | 7 |
Examples
Example 1
Complete the table of values using the formula y=2x-3.
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y |
A table of values is one way to display a linear relationship between x and y values, which means a table of values can then be created to display multiple (x,y) solutions for a given linear relation.