Slope Calculator

Slope = rise/run = (y2-y1)/(x2-x1). It measures how steep a line is and in which direction it goes. Positive slope: line goes up-right. Negative slope: line goes down-right. Zero slope: horizontal line. Undefined slope: vertical line.

y = mx + b, where m is slope and b is y-intercept. This is the most common form of a linear equation. Once you have slope and any point, you can find b: b = y - mx. For point (2,5) with slope 3: b = 5 - 3x2 = -1. Equation: y = 3x - 1.

y - y1 = m(x - x1), where m is slope and (x1,y1) is a known point. Useful when you know slope and one point but not the y-intercept. Example: slope 2, point (3,7): y - 7 = 2(x - 3) → y = 2x + 1.

Parallel lines have EQUAL slopes. Perpendicular lines have slopes that are negative reciprocals: if slope1 = m, then slope2 = -1/m. Example: slope 2/3 is perpendicular to slope -3/2. This is true for all perpendicular lines except horizontal/vertical.

Slope is rate of change. A road grade of 6% means rise 6 units per 100 units horizontal (slope = 0.06). A salary that increases $2,000 per year has slope of 2,000. Stock price change over time has slope = price change rate. In physics, slope of a distance-time graph = speed.