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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
Evaluate \(y~=~x~+~3\) at \(x~=~0\), \(1\), and \(2\), then report the complete set of matching 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

Use ordered-pair form

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

Each requested pair places the chosen input first and its evaluated output second.

02

Evaluate at zero

\[x=0~⇒~y=0+3=3~⇒~(0,3)\]

Substitute zero for x and pair it with the resulting output three.

03

Evaluate at one

\[x=1~⇒~y=1+3=4~⇒~(1,4)\]

The rule maps input one to output four.

04

Evaluate at two

\[x=2~⇒~y=2+3=5~⇒~(2,5)\]

The rule maps input two to output five.

05

Report the complete set

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

All three requested inputs appear once, with x first and its matching y second.

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Another way

  1. Make a two-column x-y table, enter 0, 1, and 2 in the x column, and add three for the y column.

!

Common mistake

Do not reverse the coordinates; the equation gives y from x, so each pair is written (x, y).

Solution walkthrough video