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Friday 12th of July
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 Dependent Variable

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# The Slope of a Line

The rise of a line represents the vertical change when moving from one point to a second point on a line.

The run of a line represents the horizontal change when moving from one point to a second point on the line.

The slope of a line is the ratio of the rise to the run. It is a number that describes the steepness of the line.

Definition

Slope of a Line

The slope of the line that passes through two points, (x1, y1) and (x2, y2), is given by slope

where x1 x2.

Example 1

Find the slope of the line that passes through the points (-2, 7) and (4, 3).

Solution

 Let (x1, y1) = (-2, 7) and (x2, y2) = (4, 3). m Substitute these values in the slope formula. Simplify. Reduce. Thus, the slope of the line through (-2, 7) and (4, 3) is .

Note:

When using the slope formula, it does not matter which point we choose for (x1, y1) and which we choose for (x2, y2).

Example 2

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

Solution

 Let (x1, y1) = (-4, 5) and (x2, y2) = (3, 5). m Substitute these values in the slope formula. Simplify. Divide. = 0 Thus, the slope of the line through (-4, 5) and (3, 5) is 0. In fact, the slope of any horizontal line is 0.