Slope (m): Rise over Run, 2-Point Formula & Linear Graphing
Slope (represented by m) measures the steepness and direction of a straight line on a 2D Cartesian coordinate plane. It is calculated as the ratio of vertical change (rise, Δy) to horizontal change (run, Δx).
🧠 Core Mental Strategies & Shortcuts
📈 Rise Over Run Staircase
Pick any two points on a line: count vertical units moved (up = +, down = −) divided by horizontal units moved (right = +, left = −).
📍 2-Point Slope Formula
m = (y₂ − y₁) / (x₂ − x₁). Always keep coordinate pairs in consistent order to avoid sign errors.
⚡ Slope-Intercept Form (y = mx + b)
In y = mx + b, m is the slope (rate of change) and b is the y-intercept (where the line crosses the y-axis at (0, b)).
❓ Frequently Asked Questions
What is the difference between zero slope and undefined slope?
A horizontal line has zero slope (m = 0, flat ground with no rise). A vertical line has undefined slope because you cannot divide by zero run (Δx = 0).
What does a negative slope look like?
A negative slope (m < 0) slopes downward from left to right like going downhill. A positive slope (m > 0) climbs uphill from left to right.
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