Game Development Reference
In-Depth Information
Figure 6.6
The ratio of the rise to the run of a linear function does not change.
1 unit. As Figure 6.7 illustrates, as long as the slope does not change, whether the
slope is 1,
1, 4, or
4 makes no difference. The function remains linear.
Slopes That Do Change
As a momentary contrast with linear functions, consider at this point the graph of
a function that generates a line with a slope that does change. Figure 6.8 illustrates
a curve that you can generate using a quadratic equation. The lower part of the
curve reveals a slope of approximately 1. For every one unit on the
y
axis,
the lower part of the curve moves one unit on the
x
axis. However, after the line
climbs past 1 on the
y
axis, the slope changes. For one unit on the
x
axis, the line
climbs 3 units on the
y
axis. The slope for this part of the curve is approximately 3.
In this respect, then, the line does not reveal the work of a linear function.
