Determine rate of change from a table

Rate of change from a table is determined by dividing the change in the output by the corresponding change in the input, $\frac{\Delta y}{\Delta x}$ , including when input intervals are unequal. A constant ratio indicates a linear relationship and represents its slope, with positive, negative, or zero values describing the direction of change; it is not generally found by dividing $y$ by $x$ . This scope excludes instantaneous rates and formal analysis of nonlinear functions.

Detailed Explanation: Determine rate of change from a table

To find the rate of change from a table, compare how much the output $y$ changes to how much the input $x$ changes:

\text{rate of change}=\frac{\Delta y}{\Delta x} =\frac{\text{change in }y}{\text{change in }x}

Use two rows from the table.

$x$	$y$
$2$	$7$
$5$	$16$
$9$	$28$

Step 1: Choose two points.
Use the first two points: $(2,7)$ and $(5,16)$ .

Step 2: Find each change.

\Delta y=16-7=9

\Delta x=5-2=3

Step 3: Divide the changes.

\text{rate of change}=\frac{\Delta y}{\Delta x} =\frac{9}{3}=3

The rate of change is $3$ . This means that for every increase of $1$ in $x$ , $y$ increases by $3$ .

Check the next pair of points. The input changes by $4$ , and the output changes by $12$ :

\frac{28-16}{9-5}=\frac{12}{4}=3

The rate is still $3$ , so the table shows a linear relationship with a slope of $3$ .

Do not usually divide $y$ by $x$ . Instead, divide the change in $y$ by the corresponding change in $x$ .

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Determine rate of change from a table

Detailed Explanation: Determine rate of change from a table

Learn by doing: Determine rate of change from a table

Practice with unlimited practice problems

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Slope - Find Equivalent - Decimal Slope to X,Y Chart