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All courses Math Foundations · MF.GR.3 42 of 60
Generate and plot ordered pairs from rules, tables, and contexts.

Generate coordinates from a rule

Problem
Use the rule y = x + 3. Find the matching ordered pair for each input value x = 0, 1, and 2. Write your answers as ordered pairs.
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Hint

Start by substituting the first input, x = 0, into y = x + 3. Then do the same for x = 1 and x = 2.

Use the rule to find each output: y is always 3 more than x. Write each ordered pair as (x, y), not (y, x).

Solution walkthrough

01

Start with the rule and pair order

\[y~=~x~+~3;~\text{ordered}~\text{pair}~=~(x,~y)\]

For each input x, add 3 to get the output y. Then write the coordinate in input-then-output order as (x, y).

02

Find the output for x = 0

\[x~=~0~\Rightarrow~y~=~0~+~3~=~3\]

When the input is 0, the rule says to add 3, so the output is 3. That makes the pair (0, 3).

03

Find the output for x = 1

\[x~=~1~\Rightarrow~y~=~1~+~3~=~4\]

Substitute 1 for x in the rule. The output is 4, so the ordered pair is (1, 4).

04

Find the output for x = 2

\[x~=~2~\Rightarrow~y~=~2~+~3~=~5\]

Substitute 2 for x. Adding 3 gives 5, so the ordered pair is (2, 5).

05

Write the full set of ordered pairs

\[(0,~3),~(1,~4),~(2,~5)\]

These are the matching ordered pairs for x = 0, 1, and 2 using the rule y = x + 3.

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Another way

  1. Make a quick table: x-values 0, 1, 2 and then add 3 to each one to get y-values 3, 4, 5. Read across the table to write (0, 3), (1, 4), (2, 5).

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Common mistake

Writing the numbers in the wrong order, such as (3, 0) instead of (0, 3). The input x comes first and the output y comes second.