Linear Functions • Topic 3 of 7

Slope Formula

Given two points (x₁, y₁) and (x₂, y₂), the slope is m = (y₂ − y₁)/(x₂ − x₁) — the difference of the y-values over the difference of the x-values, taken in the same order. Subtract consistently: if y₂ comes first on top, then x₂ comes first on the bottom. A zero denominator means the line is vertical and the slope is undefined. The slope formula lets you find steepness from any two points on a line, on a graph, or in a table, which underpins writing the line's equation on the SAT.

✅ Solved examples

1. Find the slope through (1, 2) and (4, 11).
m = (11 − 2)/(4 − 1) = 9/3 = 3.
2. Find the slope through (2, 5) and (6, 5).
m = (5 − 5)/(6 − 2) = 0/4 = 0 (horizontal).
3. Find the slope through (0, 1) and (2, 7).
m = (7 − 1)/(2 − 0) = 6/2 = 3.
4. Find the slope through (3, 4) and (3, 9).
m = (9 − 4)/(3 − 3) = 5/0, which is undefined (vertical line).

✏️ Practice — try these, take hints as needed

1. Find the slope through (1, 1) and (5, 9).
m = (9 − 1)/(5 − 1).
8/4.
—
2.
2. Find the slope through (2, 3) and (4, 9).
m = (9 − 3)/(4 − 2).
6/2.
—
3.
3. Find the slope through (0, 0) and (5, −10).
m = (−10 − 0)/(5 − 0).
−10/5.
—
−2.
4. Find the slope through (1, 4) and (6, 4).
Numerator is 4 − 4.
0 over anything.
—
0.
5. Find the slope through (−1, 2) and (3, 10).
m = (10 − 2)/(3 − (−1)).
8/4.
—
2.

📝 Topic test — 8 questions

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