Slope from a Table

First, check that the table is linear

Look at how $y$ changes from row to row. If $x$ goes up by the same amount each time and $y$ also goes up (or down) by the same amount each time, the table is linear. If the $y$-changes grow or shrink — like $1, 4, 9, 16$, where the jumps are $3$, then $5$, then $7$ — the table is not linear and it has no single slope.

This check matters because the slope formula only means something for a line. Always glance down the $y$-column before you compute anything.

Pick two rows and use the formula

Each row of the table is a point $(x, y)$. Choose any two rows — neighbors are easiest — and plug them into $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$. Keep the rows in the same order on top and bottom.

Since the table is linear, every pair of rows gives the same slope. That makes a great self-check: compute the slope from a second pair, and if the answers disagree, you made an arithmetic slip somewhere.

Plotting the rows makes the idea concrete: because the table is linear, every $(x, y)$ row lands on the same straight line, and any two of those points give its slope.

Watch the $x$-steps

The most common mistake is reading only the $y$-column. If $y$ goes up by $6$ each row, the slope is not automatically $6$ — it is $6$ divided by however much $x$ changed. In a table where $x$ steps by $5$, a $y$-step of $6$ means the slope is $\dfrac{6}{5}$. Always divide by the change in $x$.

Worked examples

Try one yourself

Common questions