Game Development Reference
In-Depth Information
The goal here is to designate that you cannot solve the equation for
y
if the value
of
x
is less than 0.
Note
For much of the discussion in this topic, consider function and equation to be nearly
synonymous. Not all equations can be interpreted as functions, however. Generally, a function and
an equation both relate the values of a range to the values of a domain.
Linear Functions
Certain functions are linear. A linear function is a function that generates a
straight line. Here are a couple of examples of linear equations:
y ¼
2
x þ
3
4
a
3
a ¼
12
Generally, when you formally identify such equations, you use the following
expressions:
y ¼ mx þ b
Ax þ By ¼ C
In these equations,
y
and
x
represent variables. You can view
x
as representing the
domain value and
y
as representing the range value. In both cases, these are
variable values. The other letters (
m
,
b
,
A
,
B
, and
C
), represent constant values. A
constant value is a value you see literally expressed. In the first equation, 2 and 3
serve as constants. In the second equation, 4 and 3 furnish the constants.
The equation
y ¼ mx þ b
is known as the slope-intercept equation. The variable
m
identifies the slope. The letter
b
identifies the y-intercept. Here's yet another
rewriting of the equation:
value of range ¼
slope
ðvalue of domainÞþy
-
intercept
Table 6.1 provides discussion of the primary features of the slope-intercept
equation. Subsequent sections discuss the features of the equation in detail.
Slope
To understand how the slope-intercept equation works, consider the graph that
Figure 6.2 illustrates. At the top of the figure, the equation allows you to see how
constants and variable values combine to generate a straight line. When you set
