## Determining Whether the Slope of a Line is Positive, Negative, Infinite or Zero

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.

### Pattern for Sign of Slope

 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 (-). 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.

### Two Other Cases to Consider

 When the line is horizontal: When the line is vertical: 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. 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.