Learn about the slope of a line, a measure of its steepness and direction in coordinate geometry, calculated as the ratio of vertical change to horizontal change.
The slope of a line is a measure of how steep the line is. It is defined as the ratio of the vertical change between two points on the line to the horizontal change between those same two points. In other words, the slope is the rise divided by the run. It represents the rate at which the line is moving either upward or downward.
The formula to calculate the slope of a line passing through two points (x1, y1) and (x2, y2) is:
( ext{slope} = dfrac{y_2 - y_1}{x_2 - x_1} )
If the slope is positive, it means the line is going upward from left to right. If it is negative, the line is going downward. A slope equal to zero indicates a horizontal line, while an undefined slope represents a vertical line.
Understanding the slope of a line is important in various fields, including mathematics, physics, engineering, and economics. It helps in determining the direction and steepness of a line, which are crucial for various applications.
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