Skill: Write an equation from a table of values

A linear table has a constant rate of change: each time $x$ changes by the same amount, $y$ changes by the same amount.

A linear equation has the form

$$y=mx+b$$

where:

• $m$ is the slope, or rate of change
• $b$ is the value of $y$ when $x=0$

Example

Write an equation for the relationship in the table.

$x$	$y$
$0$	$5$
$1$	$8$
$2$	$11$
$3$	$14$

Step 1: Find the change in $y$.

As $x$ increases by $1$, $y$ increases by $3$ each time:

$$8-5=3,\qquad 11-8=3,\qquad 14-11=3$$

So the slope is

$$m=3$$

Step 2: Find the intercept.

Look for the row where $x=0$. The corresponding $y$-value is $5$, so

$$b=5$$

Step 3: Substitute into $y=mx+b$.

Replace $m$ with $3$ and $b$ with $5$:

$$\boxed{y=3x+5}$$

Step 4: Check the equation.

For example, when $x=2$:

$$y=3(2)+5=6+5=11$$

The table shows $y=11$ when $x=2$, so the equation matches the table.