The slope (m) between two points is calculated using the formula: m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Explanation:
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Identify the Coordinates: You need the coordinates of two points, usually written as (x₁, y₁) and (x₂, y₂).
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Apply the Formula: Plug the coordinate values into the slope formula: m = (y₂ - y₁) / (x₂ - x₁).
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Calculate the Change in Y (Rise): Subtract the y-coordinate of the first point (y₁) from the y-coordinate of the second point (y₂). This gives you the vertical change, often referred to as the "rise."
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Calculate the Change in X (Run): Subtract the x-coordinate of the first point (x₁) from the x-coordinate of the second point (x₂). This gives you the horizontal change, often referred to as the "run."
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Divide Rise by Run: Divide the change in y (rise) by the change in x (run). The result is the slope (m).
Example:
Let's say you have two points: (1, 2) and (4, 8).
- (x₁, y₁) = (1, 2)
- (x₂, y₂) = (4, 8)
Using the formula:
m = (8 - 2) / (4 - 1) = 6 / 3 = 2
Therefore, the slope of the line passing through the points (1, 2) and (4, 8) is 2.
In Summary: Finding the slope between two points is a straightforward calculation involving the difference in y-coordinates divided by the difference in x-coordinates. This calculation reveals the steepness and direction of a line.
