Game Development Reference
In-Depth Information
Exercise Set 6.1
For each line, find the slope and y-intercept. Graph the line.
a. y ¼ 4x þ 3
b. y ¼2x 2
c. y ¼2x þ 3
d. y ¼ 3x 2
e. y ¼5x þ 5
f. y 3 ¼ 5
3
g. y ¼
7
x þ 5
9
h. y ¼
4
x 7
i. y ¼
2
5
x
3
j. y ¼
8
x þ 6
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.
You can express the ratio of the rise to the run of a linear function using the
capital letter delta (
D
) from ancient Greek:
rise
run
¼
D
y
slope ¼ m ¼
x
In Figure 6.6, to make it easier to view the ratio, you measure the rise and the run
of the line with triangles with a height of 2 and a base of 2, but the slope (
m
)
throughout remains 1. In other words, for each rise of 1 unit, the line runs by
D
