5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 8, 2018 13:46

Review of Precalculus 47

Example 1

Write an equation of the line through the points (−2, 1) and (3,−9).

The slope of line passing through (−2, 1) and (3,−9) ism=

− 9 − 1

3 −(−2)

=

− 10

5

=−2. Using

the point-slope form and the point (−2, 1),

y− 1 =−2(x−(−2))

y− 1 =−2(x+2) ory=− 2 x− 3

An equation of the line isy=− 2 x−3.

Example 2

An equation of a linelis 2x+ 3 y=12. Find the slope, thex-intercept, and they-intercept
of linel.

Begin by expressing the equation 2x+ 3 y=12 inslope-intercept form.

2 x+ 3 y= 12

3 y=− 2 x+ 12

y=

− 2

3

x+ 4

Therefore,m, the slope of linel,is

− 2

3

andb, they-intercept, is 4. To find thex-intercept,

sety=0 in the original equation 2x+ 3 y=12. Thus, 2x+ 0 =12 andx=6. Thex-intercept
of linelis 6.

Example 3

Equations ofverticalandhorizontallines involve only a single variable. Figure 5.1-2 shows
several examples:
y

0 x

x = − (^4) x = 2
− 4 2
y
0 x
2 y = 2
y = − 3
− 3
Figure 5.1-2
Parallel and Perpendicular Lines
Given two nonvertical linesl 1 andl 2 with slopesm 1 andm 2 , as shown in Figure 5.1-3,
respectively, they are parallel if and only ifm 1 =m 2.
y l 1 l 2
0 x
Figure 5.1-3