Calculating your slope (m) is straightforward once you know the Slope formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Slope Calculator.
What is Slope?
The Slope calculation tells you your slope (m) from a few simple inputs. The figure you are solving for here is the slope (m).
The Slope formula
The core formula is:
Slope (m) = (y₂ - y₁) ÷ (x₂ - x₁)Here is what each input means:
- x₁ — a number. Example: 1.
- y₁ — a number. Example: 2.
- x₂ — a number. Example: 3.
- y₂ — a number. Example: 8.
How to calculate it step by step
- Write down the x₁ (for example, 1).
- Write down the y₁ (for example, 2).
- Write down the x₂ (for example, 3).
- Write down the y₂ (for example, 8).
- Apply the formula above to get your slope (m).
- Double-check the result with the Slope Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| x₁ | 1 |
| y₁ | 2 |
| x₂ | 3 |
| y₂ | 8 |
| Slope (m) | 3.0000 |
| Y-intercept (b) | -1.0000 |
| Distance between points | 6.3246 |
With x₁ of 1, y₁ of 2, x₂ of 3 and y₂ of 8, the slope (m) works out to 3.0000.
Example 2
With x₁ of 2, y₁ of 2, x₂ of 3 and y₂ of 8, the slope (m) works out to 6.0000.
| Result | Value |
|---|---|
| Slope (m) | 6.0000 |
| Y-intercept (b) | -10.0000 |
| Distance between points | 6.0828 |
Example 3
With x₁ of 5, y₁ of 2, x₂ of 3 and y₂ of 8, the slope (m) works out to -3.0000.
| Result | Value |
|---|---|
| Slope (m) | -3.0000 |
| Y-intercept (b) | 17.0000 |
| Distance between points | 6.3246 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Slope Calculator does it instantly, for free, with the formula and a worked example built in.
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