Robotics with the Boe-Bot text v2.2

Page 324 · Robotics with the Boe-Bot
)xx(
)yy(
m
)xx(m)yy(
)bmxy(
bmxy
12
12
1212
11
22
−
−
=
−=−
−−−−−−−−−−−−−
+=−
+=
Once you’ve solved for m, you can plug m back into either of the two y = mx + b
equations you started with to get b.
22
22
mxyb
bmxy
−=
+=
So, the two equations for solving for m and b turn out to be:
)xx(
)yy(
m
12
12
−
−
=
and
22
mxyb −=
Let’s plug our sample values from Table F-2 into the equations and see what the scale
factor (m) and offset constant (b) will be for the left photoresistor. First, calculate m:
37.1
116
159
m
)36152(
)56215(
m
)xx(
)yy(
m
12
12
==
−
−
=
−
−
=
Then, use m, y
2,
and x
2
to calculate b:
7b
76.6b
)15237.1(215b
≈
=
×−=