Calculating Slope: Understanding the Slope Formula and How to Find the Inclination of a Straight Line

slope formula

The slope formula is used to calculate the measure of the inclination or steepness of a straight line

The slope formula is used to calculate the measure of the inclination or steepness of a straight line. It compares the change in the y-coordinates (vertical change) to the change in the x-coordinates (horizontal change) between two points on a line.

The slope formula is:

m = (y₂ – y₁) / (x₂ – x₁)

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

To find the slope using the formula, follow these steps:

1. Identify the coordinates of the given points (x₁, y₁) and (x₂, y₂).
2. Substitute the values into the formula.
3. Calculate the difference in y-coordinates (y₂ – y₁).
4. Calculate the difference in x-coordinates (x₂ – x₁).
5. Divide the difference in y-coordinates by the difference in x-coordinates.

Let’s illustrate the slope formula with an example:

Given the points (2, 4) and (6, 10), find the slope.

Using the formula:
m = (y₂ – y₁) / (x₂ – x₁)

Substituting the values:
m = (10 – 4) / (6 – 2)

Calculating the differences:
m = 6 / 4

Simplifying the fraction:
m = 3/2 = 1.5

Therefore, the slope of the line passing through the points (2, 4) and (6, 10) is 1.5.

Remember, the slope indicates how steep the line is. A positive slope means the line rises as you move from left to right, while a negative slope means the line descends. A slope of zero represents a horizontal line, and an undefined slope represents a vertical line.

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