Slope measures how steep a line is. It is the ratio of vertical change (rise) to horizontal change (run). If a line rises 2 units for every 3 units to the right, the slope is 2/3. Horizontal lines have slope 0; vertical lines have undefined slope.

In the equation y = mx + b, m is the slope. A positive slope means the line goes up from left to right; a negative slope means it goes down. The steeper the line, the larger the absolute value of the slope.

Slope appears in algebra, calculus, and applications. The derivative of a function gives the slope of the tangent line. In physics, velocity is the slope of a position-time graph. In economics, marginal cost is a slope. The concept connects algebra and calculus.

• Rise over run
• In y = mx + b, m is the slope
• Positive, negative, zero, or undefined
• Derivative gives slope of tangent line