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Beginning Pre-Calculus for Game Developers by Boris Meltreger, John P. Flynt

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What Makes a Function Linear?

In the graphs presented in the previous sections, you worked with straight lines defined by different slope and y-intercept values. In each instance, the line you generated sloped upward into quadrant I or downward into quadrant IV, depending on whether you assigned a negative or positive value to the slope constant (m). The slope of a function is defined as the ratio between its rise and run. As Figure 6.6 illustrates, a key defining feature of functions identified as linear is that regardless of the position at which you examine a line you generate using a linear function, the ratio of the rise to the run remains the same.

Figure 6.6. The ratio of the rise to the run of a linear function does not change.

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