Slope from two points

Rise over run — the change in y divided by the change in x.

The question

Find the slope of the line through (2, 3) and (6, 11)

The trick

Slope = (y₂ − y₁) ÷ (x₂ − x₁). Subtract the y's, subtract the x's in the same order, then divide.

Worked example

1Change in y: 11 − 3 = 8
2Change in x: 6 − 2 = 4
3Slope = 8 ÷ 4 = 2

So: 2

Remember it like this

Rise over run. Y is up, so y goes on top.

In the exam

Keep the order consistent — if you start with the second point's y, start with the second point's x too. Flipping one and not the other gives you the right number with the wrong sign, which costs the mark.

Why it works

Slope measures how steeply the line climbs: how far up it goes for each step across. That is exactly the vertical change divided by the horizontal change.

Explain this to my childGet the words to teach it, in your language

Try it yourself

0/3 correct

1
Slope through (1, 2) and (4, 8)
Slope through (1, 2) and (4, 8)
2
Slope through (0, 0) and (3, 9)
Slope through (0, 0) and (3, 9)
3
Slope through (2, 5) and (6, 5)
Slope through (2, 5) and (6, 5)