The slope equation is used in coordinate geometry to determine the steepness or incline of a line on a graph. The slope is a measure of how much a line rises (or falls) vertically for each unit of horizontal movement. It is a key concept in understanding linear relationships between variables.
Formula for Slope Equation
The slope of a line can be calculated using the formula: m = (y2 – y1) / (x2 – x1), where ‘m’ is the slope, and (x1, y1) and (x2, y2) are the coordinates of any two points on the line.
How to Use the Slope Equation
- Choose two points on the line. These points can be represented as (x1, y1) and (x2, y2).
- Calculate the change in the y-coordinates, which is y2 – y1.
- Calculate the change in the x-coordinates, which is x2 – x1.
- Divide the change in y-coordinates by the change in x-coordinates to find the slope.
Example 1: Calculating Slope with Two Points
Find the slope of a line passing through the points (2, 3) and (4, 7).
Calculation: m = (7 – 3) / (4 – 2) = 4 / 2 = 2. Therefore, the slope of the line is 2.
Interpreting Slope
A positive slope indicates that the line rises as it moves from left to right. A negative slope means the line falls as it moves from left to right. A slope of zero indicates a horizontal line, and an undefined slope (when x-coordinates are the same) indicates a vertical line.
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