Skill: 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.