How do I find the slope of a line given two points?
The slope of a line measures how steep it is and is found by calculating the ratio of vertical change to horizontal change between two points. Given two points (x₁, y₁) and (x₂, y₂), you can find the slope using a simple formula.
Steps
Identify your two points and label them as (x₁, y₁) and (x₂, y₂). It doesn't matter which point you call point 1 or point 2.
Find the vertical change by subtracting the y-coordinates: y₂ - y₁. This is called the rise.
Find the horizontal change by subtracting the x-coordinates: x₂ - x₁. This is called the run.
Divide the rise by the run using the slope formula: m = (y₂ - y₁)/(x₂ - x₁).
Simplify your answer if possible. A positive slope means the line goes up from left to right, while a negative slope means it goes down.
Worked example
Let's find the slope between points (2, 3) and (6, 11). Using the formula: m = (11 - 3)/(6 - 2) = 8/4 = 2. The slope is 2, meaning for every 1 unit you move right, the line goes up 2 units.
Remember
Slope is rise over run, calculated as the change in y divided by the change in x between any two points on a line.