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Slope

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slope = m =

Slope

The slope of a line is the ratio of the vertical change to the horizontal change between any two points on the line.

As a formula,

Here, (x1, y1) and (x2, y2) are two points on the line.

Example 1:

Find the slope of the line that contains the points (- 5, 3) and (4, 0).

Here, x1 = - 5, y1 = 3, x2 = 4, and y2 = 0.

In example 1,

means the line falls1 unit (because of the negative) for every three units to the right as shown by the red arrows on the graph.

Geometric Interpretation of slope:

Example 2:

Find the slope of the line that contains the points (- 1, 3) and (- 1, - 2).

which is undefined.

In example two, the slope was found to be undefined. Here the two points lie on a vertical line.

Facts About Special Lines

The slope of a vertical line is undefined.

The slope of a horizontal line is zero.

Slopes of lines:

Slopes of lines:

Slopes of lines:

Slopes of lines:

Slopes of lines:

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