Generate ordered pairs from a rule

A rule relates an input $x$ to an output $y$ , and an ordered pair $(x,y)$ records the corresponding values in that order. The understanding includes substituting whole-number or simple integer inputs into an expression such as $y=2x+3$ , generating and checking pairs in a table, and recognizing that the pairs may be plotted as points representing the relationship. Formal function notation, unrestricted domains, and more advanced rule types are not included.

Detailed Explanation: Generate ordered pairs from a rule

A rule tells you how to find an output $y$ from an input $x$ . An ordered pair is written as $(x,y)$ :

The first number is the input, $x$ .
The second number is the output, $y$ .

Example

Use the rule

y=2x+3

Find the ordered pairs when $x=0,1,2,$ and $3$ .

For each input, substitute the value for $x$ and calculate $y$ .

Input $x$	Substitute into $y=2x+3$	Output $y$	Ordered pair
$0$	$y=2(0)+3$	$3$	$(0,3)$
$1$	$y=2(1)+3$	$5$	$(1,5)$
$2$	$y=2(2)+3$	$7$	$(2,7)$
$3$	$y=2(3)+3$	$9$	$(3,9)$

So the ordered pairs are

(0,3),\ (1,5),\ (2,7),\ (3,9).

To check a pair, substitute its first number into the rule and see whether you get its second number. For example, for $(2,7)$ :

2(2)+3=4+3=7

The pair is correct. These ordered pairs can also be plotted as points on a coordinate grid. Each point is plotted using $x$ first and $y$ second.

Learn by doing: Generate ordered pairs from a rule

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Input/Output Tables (Multiply then Add/Subtract) - Table with Gap to Missing Value

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