Determine slope from a table

A table of corresponding $x$ - and $y$ -values represents a linear relationship when the ratio of the change in $y$ to the change in $x$ , $\Delta y/\Delta x$ , is constant; this rate of change is the slope and may be positive, negative, or zero. The slope can be determined from any two ordered pairs in the table, including when $x$ -values are not consecutive, while distinguishing it from $y/x$ or from the un-reversed change in $x$ ; more advanced treatments of nonlinear data or undefined slope are not included.

Detailed Explanation: Determine slope from a table

Slope tells how much $y$ changes for each change in $x$ . For a table, use two corresponding ordered pairs and calculate

m=\frac{\Delta y}{\Delta x} =\frac{y_2-y_1}{x_2-x_1}.

Always subtract in the same order: if you use the second $y$ minus the first $y$ , also use the second $x$ minus the first $x$ .

Suppose the table shows:

$x$	$y$
$1$	$5$
$3$	$9$
$6$	$15$

Step 1: Choose two points.
Use $(1,5)$ and $(6,15)$ . The $x$ -values do not need to be next to each other in the table.

Step 2: Find the change in $y$ .

\Delta y=15-5=10

Step 3: Find the change in $x$ .

\Delta x=6-1=5

Step 4: Divide the change in $y$ by the change in $x$ .

m=\frac{\Delta y}{\Delta x}=\frac{10}{5}=2

The slope is $\boxed{2}$ . This means that for every increase of $1$ in $x$ , $y$ increases by $2$ .

Do not calculate $\frac{y}{x}$ ; slope is the ratio of the changes, $\frac{\Delta y}{\Delta x}$ . Since the table represents a linear relationship, any two points should give the same slope.

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Determine slope from a table

Detailed Explanation: Determine slope from a table

Learn by doing: Determine slope from a table

Practice with unlimited practice problems

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Algebra - Find Equivalent - X,Y Chart to Function