Table of values

Given two variables, $$x and $$y, is there a way to show how these two variables are related? At the very least, we may be able to see certain values of $$y that occur at certain values of $$x. We can collect this information into a table of values.

Exploration

Imagine we started with a triangle made out of matchsticks. We can form a pattern by adding two additional matchsticks each time as shown below.

The table of values for this pattern connects the number of triangles made ($$x) with the number of matches needed ($$y).

Number of triangles ($$x)	$$1	$$2	$$3	$$4
Number of matches ($$y)	$$3	$$5	$$7	$$9

As we saw before, a table of values may be used to describe a pattern. However, we may also be given an equation or a rule to describe the relationship between two variables. Let's take a look below.

Worked example

Consider the equation $$y=3x−5. Using this rule, we want to complete the following table of values.

$$x	$$1	$$2	$$3	$$4
$$y	$$	$$	$$	$$

Think: We wish to find the value of $$y at each value of $$x in the table of values.

Do: First we find the value of $$y when $$x=1 by substitution.

Substituting $$x=1 into $$y=3x−5 we end up with:

$$y=3×(1)−5

Which simplifies to give:

$$y=−2

So after finding the value of $$y when $$x=1, we have:

$$x	$$1	$$2	$$3	$$4
$$y	$$−2	$$	$$	$$

Reflect: In general, we can complete a table of values by repeating this process of substitution for each variable given in the table.

Completing the rest of the table of values gives us:

$$x	$$1	$$2	$$3	$$4
$$y	$$−2	$$1	$$4	$$7

For a table of values, the values of $$x do not need to increase by one each time. We could obtain the following table of values repeating the same procedure as before:

$$x	$$1	$$3	$$5	$$9
$$y	$$−2	$$4	$$10	$$22

Practice Examples

Question 1

Question 2

QUESTION 3