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All courses Math Foundations · MF.GR.7 46 of 60
Match and compare words, tables, graphs, and simple equations that represent the same relationship.

Match a table to its rule

Problem
A table maps x-values 0, 1, 2, 3 to y-values 2, 6, 10, 14. Determine the equation represented by the table.
Relationship Table: x and y with 4 rows. Open full size
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Hint

Look at the row where x = 0 to find the starting value, then check how much y increases each time x goes up by 1.

A table and an equation match only if they have the same starting value and the same rate of change.

Solution walkthrough

01

Read the starting value from the table

\[x~=~0~\text{gives}~y~=~2\]

In a linear rule, the value of y when x = 0 is the starting value. So this relationship starts at 2.

02

Find the rate of change

\[2~→~6~→~10~→~14~=~+4~\text{each}~\text{time}~x~\text{increases}~\text{by}~1\]

The y-values go up by 4 for every increase of 1 in x, so the rule must have a rate of 4.

03

Compare the table to each equation

\[\begin{aligned} A:~y~=~4x~+~2~\text{has}~\text{rate}~4~\text{and}~\text{start}~2 \\ B:~y~=~2x~+~4~\text{has}~\text{rate}~2~\text{and}~\text{start}~4 \\ C:~y~=~4x~\text{has}~\text{rate}~4~\text{and}~\text{start}~0 \\ D:~y~=~x~+~2~\text{has}~\text{rate}~1~\text{and}~\text{start}~2 \end{aligned}\]

Only choice A matches both important parts of the table: it starts at 2 and increases by 4 each step.

04

Choose and verify the match

\[\text{For}~A,~x~=~3~\text{gives}~y~=~4(3)~+~2~=~14\]

That matches the table value 14 when x = 3, so the correct equation is A, y = 4x + 2.

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Another way

  1. Substitute a few table x-values into choice A: x = 0 gives 2, x = 1 gives 6, and x = 2 gives 10. Since it matches every shown row, A is the correct rule.

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Common mistake

Choosing y = 4x because the y-values are close to multiples of 4. That rule has starting value 0, but the table shows y = 2 when x = 0, so it does not match.