To find the slope of a line on a graph, you need to select two distinct points on that line and apply a simple formula. Here’s how:
Step-by-Step Guide
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Identify Two Points:
- Choose any two points on the line where the coordinates are clear and easy to read.
- Represent these points as (x₁, y₁) and (x₂, y₂). The order in which you choose them does not affect the result.
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Apply the Slope Formula:
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The formula to calculate the slope (represented by m) is:
m = (y₂ - y₁) / (x₂ - x₁)
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Here's what each part of the formula represents:
- y₂ is the y-coordinate of your second point.
- y₁ is the y-coordinate of your first point.
- x₂ is the x-coordinate of your second point.
- x₁ is the x-coordinate of your first point.
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Calculate:
- Subtract y₁ from y₂ to get the change in y.
- Subtract x₁ from x₂ to get the change in x.
- Divide the change in y by the change in x. The result is the slope m.
Example
Let's say you have two points on a line:
- Point 1: (1, 2) -- so x₁ = 1 and y₁ = 2
- Point 2: (3, 6) -- so x₂ = 3 and y₂ = 6
Using the slope formula:
m = (6 - 2) / (3 - 1) = 4 / 2 = 2
The slope of this line is 2.
Key Takeaways
- Positive Slope: A line with a positive slope goes upwards from left to right.
- Negative Slope: A line with a negative slope goes downwards from left to right.
- Zero Slope: A horizontal line has a slope of 0.
- Undefined Slope: A vertical line has an undefined slope (the denominator in the formula is 0).
| Feature | Description |
|---|---|
| Points Needed | Two distinct points on the line |
| Formula | m = (y₂ - y₁) / (x₂ - x₁) |
| Calculation | Change in y divided by the change in x |
| Positive Slope | Line goes upwards from left to right |
| Negative Slope | Line goes downwards from left to right |
| Zero Slope | Horizontal Line |
| Undefined Slope | Vertical line |
By following these steps, you can easily determine the slope of any straight line on a graph.
