Slope-Intercept Form (y = mx + b) Explained With Examples
Every straight line can be written as y = mx + b. Here is what m and b mean and how to find them.
In y = mx + b: m is the slope (steepness and direction of the line) and b is the y-intercept (where the line crosses the y-axis). If m = 2, the line rises 2 units for every 1 unit it moves right. If b = 3, the line crosses the y-axis at the point (0, 3).
Finding the Equation From Two Points
Given points (2, 5) and (6, 13): Step 1: Find slope. m = (13-5)/(6-2) = 8/4 = 2. Step 2: Plug one point into y = mx + b to find b. 5 = 2(2) + b → 5 = 4 + b → b = 1. Step 3: Write the equation. y = 2x + 1. Verify with the other point: 13 = 2(6) + 1 = 13. Correct.
Parallel and Perpendicular Lines
Parallel lines have the same slope (m₁ = m₂). Perpendicular lines have negative reciprocal slopes (m₁ × m₂ = -1). A line with slope 3 is perpendicular to a line with slope -1/3. This relationship is used constantly in geometry, physics, and engineering.