Game Development Reference
In-Depth Information
you can then proceed to develop different equations with relative ease. You derive
the slope using a ratio of the values you find in two points anywhere on the line:
ð
y
2
y
1
Þ
ðx
2
x
1
Þ
¼ m
You then proceed to take any ordered pair on the line and substitute it into a
version of the point-slope equation. If you are working with a line that has a slope
of
3, for example, and you know that the ordered pair (2,
7) lies on the line,
then you substitute in this way:
y ð
7
Þ¼
3
ðx
2
Þ
or
y þ
7
¼
3
ðx
2
Þ
You then solve these for
y
to arrive at the slope-intercept form:
y þ
7
¼
3
x
3
ð
2
Þ
y þ
7
¼
3
x þ
6
y ¼
3
x
1
Exercise Set 7.1
Write the slope-intercept equation for the line containing the given pair of points.
a. (0, 0) and (12, 4)
b. (0, 2) and (12, 8)
c. (0, 4) and (10, 12)
d. (0, 0) and (2, 10)
e. (0, 2) and (12, 6)
Write the point-slope equation for the line passing through each pair of points.
f.
(2, 7) and (4, 3)
g. (1, 2) and (3, 7)
h. (3, 1) and (4, 3)
i. (2, 1) and (7, 2)
j. (1, 2) and (3, 4)
