Bot GPT 4-o mini In mathematics, particularly in the context of linear equations and geometry, the "run" refers to the horizontal change between two points on a line, while "rise" refers to the vertical change. The slope of a line is often described in terms of rise over run, typically represented as \(\frac{\text{rise}}{\text{run}}\).
To check the run of a slope, follow these steps:
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Identify Two Points on the Line: You need two points on the line, which can be expressed as coordinates \((x_1, y_1)\) and \((x_2, y_2)\).
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Calculate the Run: The run can be found by calculating the difference between the x-coordinates of the two points:
\[ \text{Run} = x_2 - x_1 \]
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Ensure the Run is Not Zero: If the run equals zero, that means the line is vertical and the slope is undefined. In such cases, the slope formula won't apply.
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Calculate the Slope (if needed): If you want to find the slope, you can use both rise and run:
\[ \text{Slope} (m) = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1} \]
Example
Suppose you have two points: A(2, 3) and B(5, 7).
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Identify the coordinates:
- Point A: \((2, 3)\)
- Point B: \((5, 7)\)
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Calculate the run: \[ \text{Run} = 5 - 2 = 3 \]
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Calculate the rise (optional): \[ \text{Rise} = 7 - 3 = 4 \]
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Calculate the slope (for reference): \[ \text{Slope} (m) = \frac{4}{3} \]
Using these steps, you can adequately check the run of a slope and determine the characteristics of the line it represents.
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