slope
The slope is a common concept in mathematics that measures the steepness or inclination of a line
The slope is a common concept in mathematics that measures the steepness or inclination of a line. It indicates how much the y-coordinate changes for each unit increase in the x-coordinate.
To find the slope of a line, you need to know two coordinate points on the line. Let’s denote them as (x₁, y₁) and (x₂, y₂).
The formula to calculate the slope is:
slope = (y₂ – y₁) / (x₂ – x₁)
Here’s an example to illustrate how to find the slope:
Given the points A(2, 4) and B(5, 9), we want to find the slope of the line passing through these two points.
Using the slope formula:
slope = (y₂ – y₁) / (x₂ – x₁)
= (9 – 4) / (5 – 2)
= 5 / 3
Therefore, the slope of the line passing through points A(2, 4) and B(5, 9) is 5/3.
The slope can be positive, negative, zero, or undefined depending on the direction and inclination of the line.
A positive slope indicates an upward direction (from left to right), a negative slope indicates a downward direction, a zero slope indicates a horizontal line, and an undefined slope indicates a vertical line.
It’s important to note that if you have two vertical points with the same x-coordinate (e.g., (2, 3) and (2, 5)), the slope is undefined, since division by zero is not defined in mathematics. In this case, the line is vertical.
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