Game Development Reference
In-Depth Information
line, you see another line. The second line has a negative slope. It slopes
downward, into quadrant IV. It passes through the y-intercept (0, 2). Among the
points in its path are (3, 1) and, as mentioned previously, (6, 0). The second line
is perpendicular to the line with the positive slope.
To investigate the features of the perpendicular line, consider the expression you
use to determine the slope of a line:
y
2
y
1
x
2
x
1
To make use of this expression, you can substitute the values given by the two
ordered pairs as follows:
2
1
0
3
¼
1
3
This gives you the slope of the second line (
3
), and given that you know the slope
of the second line, you can then write the following slope-intercept equation:
1
3
x þ
2
y ¼
You then have at hand an equation you can use to determine the point at which
the line crosses the
x
axis. Toward this end, you can rewrite the equation so that
you set
y
to 0 and solve for
x
:
1
3
x þ
2
¼
0
1
3
x ¼
2
x ¼ð
2
Þð
3
Þ
1
3
ð
3
Þ
x ¼
6
To explore this notion from a slightly different perspective, here is an equation
that provides the following negative slope:
y ¼
2
3
x þ
4
