Find the slope from two points
Slope is the measure of a line's steepness. It's the 'rise over run'. You don't always need a graph to find it; if you have any two points on the line, you can use a simple formula to calculate the slope.
Do this: Read the concept below, then try the quiz or activity.
Concept
The slope of a line, often represented by the variable 'm', measures its steepness. It is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
The Slope Formula Given two points, (x₁, y₁) and (x₂, y₂):
m = (y₂ - y₁) / (x₂ - x₁) = Rise / Run
Understanding the Formula: * y₂ - y₁ (Rise): The change in the vertical direction. How much did the line go up or down? * x₂ - x₁ (Run): The change in the horizontal direction. How much did the line go left or right?
Steps to Find the Slope:
1. Label your points: Identify (x₁, y₁) and (x₂, y₂). It doesn't matter which point you call "1" and which you call "2", as long as you are consistent. 2. Substitute the values into the slope formula. 3. Simplify the fraction to find the slope.
Example: Find the slope between the points (2, 3) and (6, 11).
1. Label:
* (x₁, y₁) = (2, 3)
* (x₂, y₂) = (6, 11)
2. Substitute:
* m = (11 - 3) / (6 - 2)
3. Simplify:
* m = 8 / 4
* m = 2
* The slope is 2. This means for every 1 unit you move to the right on the graph, you move 2 units up.Types of Slope:
* Positive Slope: The line goes up from left to right. (e.g., m = 3) * Negative Slope: The line goes down from left to right. (e.g., m = -1/2) * Zero Slope: A perfectly horizontal line. The 'rise' is 0. (e.g., m = 0) * Undefined Slope: A perfectly vertical line. The 'run' is 0, and you cannot divide by zero.
Key Idea: The slope is a single number that tells you the direction and steepness of a line. A bigger number means a steeper line.
Try it
Practice: Find the slope from two points.