Finding the slope of a line is a key concept in algebra and coordinate geometry. The slope indicates the steepness and direction of the line. It is calculated as the ratio of the vertical change (‘rise’) to the horizontal change (‘run’) between two distinct points on the line.
Steps to Find the Slope
- Select two points on the line. These can be any two points, (x1, y1) and (x2, y2).
- Calculate the ‘rise’ by finding the difference in the y-values of these points (y2 – y1).
- Calculate the ‘run’ by finding the difference in the x-values of these points (x2 – x1).
- Divide the rise by the run to get the slope. The formula is: slope (m) = (y2 – y1) / (x2 – x1).
Example 1: Finding Slope with Two Points
Find the slope of a line passing through the points (1, 2) and (3, 6).
Calculation: m = (6 – 2) / (3 – 1) = 4 / 2 = 2. Therefore, the slope of the line is 2.
Example 2: Understanding Slope Direction
A positive slope indicates the line rises as it moves from left to right. A negative slope indicates the line falls as it moves from left to right. A slope of zero means the line is horizontal, and an undefined or infinite slope means the line is vertical.
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