Understanding the Slope Formula | A Comprehensive Guide to Calculating the Steepness of a Line

Slope Formula

The slope formula is a mathematical equation that allows you to calculate the steepness of a line

The slope formula is a mathematical equation that allows you to calculate the steepness of a line. It measures how much a line rises or falls for each unit of horizontal change. The slope of a line is often represented by the letter “m” and can be positive, negative, zero, or undefined.

The slope formula is expressed as:

m = (y2 – y1) / (x2 – x1)

Where:
– m represents the slope of the line
– (x1, y1) and (x2, y2) are the coordinates of two points on the line

To use the slope formula, follow these steps:
1. Identify the coordinates of two points on the line, let’s say (x1, y1) and (x2, y2).
2. Plug the values into the formula: m = (y2 – y1) / (x2 – x1).
3. Calculate the difference between the y-coordinates (vertical change) and the difference between the x-coordinates (horizontal change).
4. Divide the vertical change by the horizontal change to get the slope, m.

For example, let’s find the slope of a line passing through the points (2, 4) and (5, 9):
– Plug the values into the formula: m = (9 – 4) / (5 – 2).
– Calculate the differences: m = 5 / 3.
– The slope of the line is 5/3 or approximately 1.67.

The slope formula is a fundamental tool in algebra and is used in various applications, such as determining the rates of change, finding the equation of a line, and analyzing linear relationships.

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