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Line Slope Value

Calculating the value of the slope is important in defining a function. This lesson will teach you how to find the value of the slope. Slope is usually represented by the variable m.

The Value of the Slope of a Line
Zero and Undefined Slope

$$Slope = m = {\frac {rise}{run}}$$

• m = the variable we use for slope
• Rise = how far up your step goes
• Run = how far over your step goes

Remember to check to see if your slope should be positive or negative.

### Practice Problems

Use the following graph to answer questions 1 through 7.
1. What is the slope of line A? (
Solution
Solution: $$\text{m} = -\dfrac{7}{2}$$
Details:

Step 1: Locate two points on the graph that will be used to find the slope. It is best to choose points with x and y values that are integers, if possible. We will choose $$(−2,3)$$ and $$(0,−4)$$.

Step 2: Draw a vertical line and a horizontal line to represent the ‘step’ between the two points:

Step 3: Find the rise (or change in y value) and the run (or change in x value).

Step 4: Find the slope. The slope is the change in y value (or how much the line went up or down between the two points) divided by the change in x value (or how much the step moves to the right). The slope is negative since it goes down when we follow the line from left to right. The slope is:

$${\text{m=}}\dfrac{\text{change in y}}{\text{change in x}}=-\dfrac{7}{2}$$

$${\text{m}}=-\dfrac{7}{2}$$
)
2. What is the slope of line B? (
Solution
Solution:
$$\text{m}=1$$
)
3. What is the slope of line C? (
Solution
Solution:
$$\text{m}=-2$$
)
4. What is the slope of line D? (
Solution
Solution:
$$\text{m} = \dfrac{1}{3}$$
)
5. What is the slope of line E? (
Solution
Solution:
$$\text{m} = -\dfrac{2}{5}$$
)
6. What is the slope of a horizontal line? (
Solution
Solution:
$$\text{m} = 0$$
)
7. What is the slope of a vertical line? (
Solution
Solution: The slope of a vertical line is undefined.
Details:

Step 1: Locate two points on the graph that will be used to find the slope. Since we don’t have a graph of this line we’ll draw a sample line and include two points so that we can find the slope:

Step 2: Draw a vertical line and a horizontal line to represent the ‘step’ between the two points. In this case, we can only draw a vertical line because there is no change in the x values:

Step 3: Find the rise (or change in y-value) and the run (or change in x-value). The rise, or change in y-value, is 2. There is no change in the x-value so the run is 0.

Step 4: Find the slope. The slope is the change in y-value (or how much the line went up or down between the two points) divided by the change in x-value (or how much the step moved to the right).

$${\text{m}}=\dfrac{\text{change in y}}{\text{change in x}}=\dfrac{2}{0}$$

So m = undefined because we can’t divide by zero.
)

## Need More Help?

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