You find the slope of a line using the slope formula by calculating the change in the y-coordinates divided by the change in the x-coordinates between two points on the line.
Here's a breakdown of how to use the slope formula:
Understanding Slope
- Slope: Represents the steepness and direction of a line. It tells you how much the line rises or falls for every unit of horizontal change.
- Rise: The vertical change between two points on a line (change in y-coordinate).
- Run: The horizontal change between two points on a line (change in x-coordinate).
The Slope Formula
The slope formula is:
slope (m) = (y₂ - y₁) / (x₂ - x₁)
Where:
- (x₁, y₁) are the coordinates of the first point.
- (x₂, y₂) are the coordinates of the second point.
Steps to Find the Slope
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Identify Two Points: Choose any two distinct points on the line. Their coordinates will be in the form (x, y).
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Label the Coordinates: Label the coordinates of the first point as (x₁, y₁) and the coordinates of the second point as (x₂, y₂). It doesn't matter which point you choose as the "first" or "second" as long as you are consistent.
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Plug the Values into the Formula: Substitute the values of x₁, y₁, x₂, and y₂ into the slope formula: m = (y₂ - y₁) / (x₂ - x₁).
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Simplify: Perform the subtraction in the numerator and denominator. Then, divide the result to find the slope (m).
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Interpret the Slope:
- Positive Slope: The line rises from left to right.
- Negative Slope: The line falls from left to right.
- Zero Slope: The line is horizontal (y₂ - y₁ = 0).
- Undefined Slope: The line is vertical (x₂ - x₁ = 0).
Example
Let's say you have two points on a line: (1, 2) and (4, 8).
- Points: (1, 2) and (4, 8)
- Label: x₁ = 1, y₁ = 2, x₂ = 4, y₂ = 8
- Plug in: m = (8 - 2) / (4 - 1)
- Simplify: m = 6 / 3 = 2
Therefore, the slope of the line is 2. This means that for every one unit you move to the right along the line, you move two units up.
