What is how to find the slope?

Finding the Slope

The slope of a line describes its steepness and direction. It is a fundamental concept in algebra and calculus. There are several ways to determine the slope:

1. Slope from Two Points

If you are given two points on a line, (x₁, y₁) and (x₂, y₂), you can calculate the slope (often denoted by 'm') using the following formula, also known as the "rise over run":

m = (y₂ - y₁) / (x₂ - x₁)

Where:

• (y₂ - y₁) represents the "rise" (the change in vertical distance).
• (x₂ - x₁) represents the "run" (the change in horizontal distance).

Example: Find the slope of the line passing through (1, 2) and (4, 8).

m = (8 - 2) / (4 - 1) = 6 / 3 = 2

The slope is 2.

2. Slope from the Slope-Intercept Form

If a line is given in the slope-intercept%20form of the equation, which is:

y = mx + b

Where:

• m is the slope of the line.
• b is the y-intercept (the point where the line crosses the y-axis).

Simply identify the coefficient of x to determine the slope.

Example: In the equation y = 3x + 5, the slope is 3.

3. Slope of Horizontal and Vertical Lines

• Horizontal Line: A horizontal line has a slope of 0. This is because the y-value does not change (the rise is 0).
• Vertical Line: A vertical line has an undefined slope. This is because the x-value does not change (the run is 0), resulting in division by zero in the slope formula.

4. Parallel and Perpendicular Lines

• Parallel Lines: Parallel lines have the same slope.
• Perpendicular Lines: Perpendicular lines have slopes that are negative reciprocals of each other. If one line has a slope of m, a line perpendicular to it will have a slope of -1/m.