Write an equation from a table of values

A table of paired $x$ - and $y$ -values represents a linear relationship when equal changes in $x$ produce a constant rate of change in $y$ ; this rate is the slope $m$ , and the value of $y$ when $x=0$ is the intercept $b$ . The learner determines and verifies an equation such as $y=mx+b$ , including proportional relationships with $b=0$ , using integer or simple rational values; nonlinear patterns and more advanced forms of equations are outside this scope.

Detailed Explanation: 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.

Learn by doing: Write an equation from a table of values

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Slope - Find Equivalent - X,Y Chart to Slope Y Intercept Form

Earned ?