What is the Slope of a Line

The slope or Rate of Change of a line is a measurement of the rate at which it rises or falls. A rising line has a positive slope whereas a falling line has a negative slope. More specifically, slope is a number that is a ratio that describes the steepness of a line. The larger the absolute value of the slope, the steeper the line and vice versa.

rise and run of the slope of a line

RISE is how much a line goes up or down.

RUN is how much a line moves left or right.

Example A line with a slop of

A slope of means that every time the line rises 2, it also runs 1.

rise and run of the slope of a line example

Types of Slope of a Stright Line

Generally, there are four types of slope of a line, namely positive, negative, zero slopes and undefined slope. Let's see in detail each type separately:

Positive Slope: rises (increasing) from left to right.

positive slope in graph

Negative Slope: falls (decreasing) from left to right.

negative slope in graph

Zero Slope: is horizontal because the rise is 0, and 0 divided by any number is 0.

zero slope in graph

Undefined Slope: is a vertical line because the run is 0, and any number divided by 0 is undefined.

undefined slope in graph

5 Things You Need to Know About Slope

  1. Any time you move UP, that is a POSITIVE RISE.

  2. Any time you move DOWN, that is a NEGATIVE RISE.

  3. Any time you move RIGHT, that is a POSITIVE RUN.

  4. Any time you move LEFT, that is a NEGATIVE RUN.

  5. The slope is the SAME everywhere on a STRAIGHT LINE.


In the graph below, the line rises 3 and runs 2.

undefined slope in graph


In the graph below, the line rises -2 and runs 3.

undefined slope in graph