The steepness or slope of a line is the ratio of the vertical change to the horizontal change.

The slope of a line can be determined if two points on that line are provided.

Algebraically, this can be calculated by the formula:

where m represents the slope, the numerator shows the y, and the

denominator indicates the x.

Example

Given the points (3, 5) and (-1, 4) are both contained on the same line,

the slope of this line is

Four Basic Types of Slope

 Positive Negative Zero Undefined

Positive Slope: the line rises to the right

Negative Slope: the line falls to the right

Zero Slope: the line is horizontal (every y-coordinate is the same)

Undefined Slope: the line is vertical (every x-coordinate is the same)

Finding Slope in Excel

Given two x-coordinates and two y-coordinates, we can also use Excel to find the slope of a line.

Parallel and Perpendicular Lines

 Parallel Lines (Slopes are Equal) Perpendicular Lines (Slopes are Opposite Reciprocals)

 for both lines m = 2 m = -1 and m = 1

Finding Slope Given a Line

Examples

Find 2 clearly defined points. Determine the necessary rise and run to get from one point to the other.

Graph 1:

Find (0, -3). In order to get from this point to (1, 1), you must rise 3 times and run 1 time.

Graph 2:

Find (0, 1). Getting from this point to (3, -1) requires that you rise -2 and run 3.