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 Dependent Variable

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# Positive and Negative Slopes

A line with a positive slope slants upward as we move from left to right on the graph.

Each line shown has a positive slope.

To verify this, we can choose any two points on a line and find the slope.

For example, we will find the slope of line A. Example 1

Find the slope of line A. Solution

Choose any two points on line A.

For example, choose (-2, -5) and (4, 5).

 Let (x1, y1) = (-2, -5) and (x2, y2) = (4, 5). m Substitute the values in the slope formula. Simplify. Reduce. The slope of line A is a positive number, .

Line A slants upward as we move from left to right on the graph, so we expected a positive slope.

A line with a negative slope slants downward as we move from left to right on the graph.

Each line shown has a negative slope.

To verify this, we can choose any two points on a line and find the slope. For example, we will find the slope of line J.

Example 2

Find the slope of line J.

Solution

Choose any two points on line J. For example, choose (-4, 0) and (4, -6).

 Let (x1, y1) = (, 0) and (x2, y2) = (4, -6). m Substitute the values in the slope formula. Simplify. Reduce. The slope of line J is a negative number,   Line J slants downward as we move from left to right on the graph, so we expected a negative slope.

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