Linear FunctionsPutting It All Together

Given any two points on a line, the slope is the rise over the run:

For the points (2, 3) and (4, 9): the run is 4−2=2 and the rise is 9−3=6, so the slope is .

Nicely done — a rise of 6 over a run of 2 gives a slope of 3.

Here is the whole idea in three steps — use the arrow to move through the recap:

A line needs just two numbers: the slope m and the intercept c.

The slope m sets the tilt — a bigger size means a steeper line.

The intercept c sets the height where the line crosses the y-axis.

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Press the button to trace how a line climbs: for every step to the right (the run), it rises by a fixed amount (the rise).

Curvingo can embed static figures, galleries, and video too. Here is a figure and a small gallery:

Every straight line is a function — one input gives exactly one output.

A short walkthrough video (x−video) would sit here — drop an intro.mp4 into this chapter folder to enable it.

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In your own words, explain what changes on the graph when you increase the intercept c while keeping the slope fixed.

You have now met every core building block of a linear function — and every interactive component Curvingo has to offer.

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