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.
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.