Definition
Slope
Slope compares a line’s vertical change with its horizontal change.
What it means
Move from one point on a line to another. Count how much y changes, then divide by how much x changes. A slope of 2 means the line goes up 2 units for every 1 unit moved right. Use the same point order in both changes so the signs stay consistent.
Remember it
Slope is rise ÷ run: vertical change divided by horizontal change.
Example
From (2, 1) to (5, 7), the rise is 7 − 1 = 6 and the run is 5 − 2 = 3. The slope is 6 ÷ 3 = 2.
Watch for
A vertical line does not have slope 0. Its horizontal change is 0, so division by zero makes the slope undefined.
Common mix-up
Do not divide run by rise. Slope is vertical change divided by horizontal change.
Exact meaning
For two distinct points on a non-vertical line, slope is the change in y divided by the change in x, often called rise divided by run. Positive and negative slopes show direction, a horizontal line has slope 0, and a vertical line has undefined slope.