Game Development Reference
In-Depth Information
Having solved the equation for
b
, you can then substitute the values of the slope
and
b
(the y-intercept) into the original slope-intercept equation to create the
equation for your line:
y ¼
2
x þ
3
Making It Still Easier
In Chapter 6, you also dealt with the ratio that exists between the rise and run of a
line. You expressed that ratio in this way:
m ¼
D
y
y
2
y
1
x
2
x
1
x
¼
D
The Greek letter delta signifies changes in the ratio. The ratio works for all
ordered pairs on a line. If you return to the ordered pair you dealt with in the
previous section (4, 11), you can substitute as follows:
y
11
x
4
m ¼
Since you know the slope of the function is 2, you can set up this equation:
y
11
x
4
)
2
ðx
4
Þ¼y
11
m ¼
You can then solve the equation for
y
:
2
ðx
4
Þ¼y
11
2
x
8
¼ y
11
2
x
8
þ
11
¼ y
2
x þ
3
¼ y
Again, given the basic versions of the point-slope form of a linear function,
mðx
2
x
1
Þ¼ðy
2
y
1
Þ
or
ðy
2
y
1
Þ¼mðx
2
x
1
Þ
,
