lesson
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Imagine riding a bike down a gentle street versus plunging down a steep ramp — one feels like a breezy glide, while the other gives you a thrilling rush of speed.
In mathematics, we measure this exact steepness and slant of a line using a single number called the gradient (also commonly called slope).
📊Interactive diagram
How do we turn the visual steepness of any line segment into an exact numerical value?
Rise Over Run
To find the gradient, we compare how much a line moves vertically to how much it moves horizontally.
The vertical change between two points is called the rise, while the horizontal change from left to right is called the run.
We define the gradient (m) as the ratio of these two movements:
m=runrise
📊Interactive diagram
What does calculating this look like on a real coordinate grid?
Positive Gradients
When a line goes up from left to right, both its rise and run are positive, producing a positive gradient.