How to find slope from a table
Quick answer
Pick any two rows of the table and divide the change in y by the change in x between them. If that ratio is the same for every pair of rows, the table shows a straight line and that ratio is the slope.
A table of values is a graph with the picture taken away. Each row is a point, so finding the slope works exactly like finding slope from two points.
Worked example
| x | y |
|---|---|
| 0 | 5 |
| 1 | 8 |
| 2 | 11 |
| 3 | 14 |
Take the first two rows:
- Change in y: 8 − 5 = 3
- Change in x: 1 − 0 = 1
- Slope = 3 ÷ 1 = 3
Now check another pair, say rows 2 and 4: (14 − 8) ÷ (3 − 1) = 6 ÷ 2 = 3. Same answer, so the table is linear and the slope is 3.
Finding the y-intercept from a table
Look for the row where x = 0. Its y value is the y-intercept. Here, that’s 5, so the equation is y = 3x + 5.
If the table doesn’t include x = 0, work backward using the slope. For each step you move left in x, subtract the slope from y until you reach x = 0.
When the x values jump unevenly
Tables don’t always go up by 1. Suppose x goes 2, 5, 11 and y goes 7, 13, 25:
- (13 − 7) ÷ (5 − 2) = 6 ÷ 3 = 2
- (25 − 13) ÷ (11 − 5) = 12 ÷ 6 = 2
Still a slope of 2. Always divide by the change in x, never just look at how y changes from row to row.
What if the ratios don’t match?
Then the table isn’t a straight line, and it has no single slope. A table like x = 1, 2, 3 with y = 1, 4, 9 is a curve (y = x²), where the rate of change keeps growing.
To see the same idea visually, read how to find slope from a graph.
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