Page 25 - Calculus Demystified

CHAPTER 1
Basics
12
We could just as easily have used the points S = (−1, 5) and T = (1, −5):
5 − (−5)
m = =−5.
−1 − 1
In this example, the line falls 5 units for each 1 unit of left-to-right motion. The
negativity of the slope indicates that the line is falling.
The concept of slope is undefined for a vertical line. Such a line will have any
two points with the same x-coordinate, and calculation of slope would result in
division by 0.
You Try It: What is the slope of the line y = 2x + 8?

You Try It: What is the slope of the line y = 5? What is the slope of the line
x = 3?

Two lines are perpendicular precisely when their slopes are negative reciprocals.
This makes sense: If one line has slope 5 and the other has slope −1/5 then we
see that the first line rises 5 units for each unit of left-to-right motion while the
second line falls 1 unit for each 5 units of left-to-right motion. So the lines must be
perpendicular. See Fig. 1.18(a).

y

x

Fig. 1.18(a)

You Try It: Sketch the line that is perpendicular to x+2y = 7 and passes through
(1, 4).

Note also that two lines are parallel precisely when they have the same slope.
See Fig. 1.18(b).