Up to this point in this unit, our examples all had positive slopes. Let's take a moment to look at what happens when a line has a negative slope.
Keeping in mind that the slope is given by: In the figure , the slope of the line is: The slope of this line is negative. |
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If the line is sloping upward from left to right, so the slope is positive (+). | If the line is sloping downward from left to right, so the slope is negative (-). |
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In our pizza example, a positive slope tells us that as the number of toppings we order (x) increases, the total cost of the pizza (y) also increases. | For example, as the number of people that quit smoking (x) increases, the number of people contracting lung cancer (y) decreases. A graph of this relationship has a negative slope. |
When the line is horizontal: | When the line is vertical: |
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We can see that no matter what two points we choose, the value of the y-coordinate stays the same; it is always 3. Therefore, the change in y along the line is zero. No matter what the change in x along the line, the slope must always equal zero. | In this case, no matter what two points we choose, the value of the x-coordinate stays the same; its is always 2. Therefore, the change in x along the line is zero. |
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Zero divided by any number is zero. Horizontal lines have a slope of 0. |
Since we cannot divide by zero, we say the slope of a vertical
line is infinite. Vertical lines have an infinite slope. |
You are now ready to try a practice problem. If you have already completed the first practice problem for this unit you may wish to try the additional practice.
[practice] | [additional practice] | [table of contents] | [next unit] |