What gradient actually means

Year 9

Students who have only met m as a letter in y = mx + c have usually never seen what it measures.

Most students can recite that m is the gradient. Far fewer can say what it is the gradient of, or why a steeper line has a bigger one. That gap shows up later as guesswork on every straight-line question.

Drag it and watch

Drag either dot. Make the line steeper — what happens to the rise? Now make it go downhill. What changes about the number?

The dashed triangle is the definition. Gradient is the rise divided by the run, and nothing more.

Once gradient is a triangle rather than a letter, parallel lines, perpendicular lines and rates of change all stop being separate rules to memorise.

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