Slope
Definition
How steep a line is — the ratio of vertical change to horizontal change. On a physics graph, the slope often is the answer: the slope of a position-time graph is velocity.
Symbol: · Unit: units of y per units of x (e.g., m/s)
Technical definition
The rate of change of a dependent variable with respect to an independent variable: rise over run, Δy/Δx. For a curve, the slope at a point is the slope of the tangent line there — the derivative.
Example
On a position-time graph, a steeper line means faster motion: rise (meters) over run (seconds) gives velocity in m/s. A horizontal line has zero slope — the object is not moving.
Students read the height of a graph when the question asks for the slope, or vice versa. Remember: the value at a point is read off the axis, but the slope is rise-over-run between two points. On a velocity-time graph it is the slope — not the height — that gives acceleration.