Lesson
Constructing a table of values from a given formula
A table of values is one way to display a linear relationship between $x$x and $y$y values. A linear equation can be used to generate $y$y values from given $x$x values. Therefore, a table of values can then be created to display multiple $\left(x,y\right)$(x,y) solutions for a given linear relation.
Worked example
Construct a table of values using the following equation:
$y=3x-5$y=3x−5
The table of values for this equation connects the $y$y-value that result from substituting in a variety of $x$x-values. Let's complete the table of values below:
| $x$x | $1$1 | $2$2 | $3$3 | $4$4 |
|---|---|---|---|---|
| $y$y |
To substitute $x=1$x=1 into the equation $y=3x-5$y=3x−5, replace all accounts of $x$x with $1$1.
| $y$y | $=$= | $3\left(1\right)-5$3(1)−5 |
| $=$= | $3-5$3−5 | |
| $=$= | $-2$−2 |
So then $-2$−2 must go in the first entry in the row of $y$y-values.
| $x$x | $1$1 | $2$2 | $3$3 | $4$4 |
|---|---|---|---|---|
| $y$y | $-2$−2 |
Next let's substitute $x=2$x=2 into the equation $y=3x-5$y=3x−5.
For $x=2$x=2:
| $y$y | $=$= | $3\left(2\right)-5$3(2)−5 |
| $=$= | $6-5$6−5 | |
| $=$= | $1$1 |
So then $1$1 must go in the second entry in the row of $y$y-values.
| $x$x | $1$1 | $2$2 | $3$3 | $4$4 |
|---|---|---|---|---|
| $y$y | $-2$−2 | $1$1 |
Continue with this process of substituting the remaining values of $x$x to complete the table of values:
| $x$x | $1$1 | $2$2 | $3$3 | $4$4 |
|---|---|---|---|---|
| $y$y | $-2$−2 | $1$1 | $4$4 | $7$7 |
Practice questions
Question 1
Complete the table of values using the formula $q=2p-3$q=2p−3.
$p$p $0$0 $1$1 $2$2 $3$3 $4$4 $q$q $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$