Find the slope of a graph

key notes:

What is Slope?

• The slope of a line tells how steep the line is.
• It measures the rate of change between two points on a line.
• In mathematics, slope is often denoted by the letter m.

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Formula for Slope

If you know two points on the line, (x1,y1) and (x2,y2)​​

m = y2−y1​ / x2−x1

• y2−y1​ → change in y (rise)
• x2−x1​ → change in x (run)

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Rise and Run

• Rise → how much the line goes up or down.
• Run → how much the line goes left or right.
• Slope = Rise ÷ Run

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Types of Slopes

• Positive slope → line goes upward from left to right.
• Negative slope → line goes downward from left to right.
• Zero slope → horizontal line (no rise).
• Undefined slope → vertical line (run = 0).

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Steps to Find the Slope from a Graph

• Choose any two points exactly on the line.
• Label them (x1 , y1) and (x2 , y2) .
• Find the rise (y2 − y1 and run (x2 − x1​).
• Apply the slope formula:

m = rise / runm

• Simplify the fraction if possible.

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Examples

Example 1: Points (2,3) and (5,9)

m = 9 – 3 / 5 – 2 = 6/3 = 2

Slope = 2 (positive).

Example 2: Points (4,7) and (1,10)

m = 10 – 7 / 1 – 4 = 3 / -3 = –1

Slope = –1 (negative).

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Real-life Meaning

• In real-world graphs, slope can represent speed, cost per item, rate of change in temperature, etc.
• Example: If the slope is 3, it means “for every 1 unit increase in xxx, yyy increases by 3 units.”

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Quick Tips

• Always subtract in the same order for yyy and xxx.
• Avoid switching points randomly—it changes the sign.
• Vertical line → slope undefined (division by zero).
• Horizontal line → slope = 0.

Learn with an example

Let’s Practice!