Find the slope from two points

key notes:

What is Slope?

• Slope tells us how steep a line is.
• It shows how much the y-value changes for every change in the x-value.
• Slope is also called the rate of change or gradient.

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Formula for Slope

If two points on a line are (x₁, y₁) and (x₂, y₂), the slope (m) is:

​m = y2 − y1 / x2 − x1

Read as:
Slope = Change in y ÷ Change in x
or
Slope = rise ÷ run

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Steps to Find the Slope

1. Label the points: (x₁, y₁) and (x₂, y₂)
2. Subtract y-values: y2−y1​ → this is the rise.
3. Subtract x-values: x2−x1→ this is the run.
4. Divide: rise / run
5. Simplify the fraction if possible.

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Example

Find the slope of the line passing through (2, 5) and (6, 13):

m = 13−5 / 6−2 = 8/4 = 2

Slope = 2 → For every 1 unit you move right, the line goes up by 2 units.

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Types of Slope

• Positive slope: Line goes up from left to right.
• Negative slope: Line goes down from left to right.
• Zero slope: Horizontal line (no rise).
• Undefined slope: Vertical line (no run).

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Common Mistakes

• Mixing up x and y values.
• Forgetting to subtract in the same order for both numerator and denominator.
• Dividing by zero (happens in vertical lines → slope is undefined).

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Real-life Connection

• Slope is used in roads, ramps, roofs, and graphs to show steepness or rate of change.

Learn with an example