Page 21 - Calculus Demystified

8 CHAPTER 1 Basics

k

Fig. 1.10

y

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x

Fig. 1.11

1.4 The Slope of a Line in the Plane

A line in the plane may rise gradually from left to right, or it may rise quite steeply
from left to right (Fig. 1.13). Likewise, it could fall gradually from left to right,
or it could fall quite steeply from left to right (Fig. 1.14). The number “slope”
differentiates among these different rates of rise or fall.
Look at Fig. 1.15. We use the two points P = (p 1 ,p 2 ) and Q = (q 1 ,q 2 ) to
calculate the slope. It is
q 2 − p 2
m = .
q 1 − p 1

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