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

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

48 STEP 4. Review the Knowledge You Need to Score High

Linesl 1 andl 2 are perpendicular if and only ifm 1 m 2 =−1. (See Figure 5.1-4.)

l 1 l^2

y

0 x

Figure 5.1-4

Example 1

Write an equation of the line through the point (−1, 3) and parallel to the line 3x− 2 y=6.

(See Figure 5.1-5.)

y

0 x

3 x − 2 y = 6

(−1, 3)

− 3

Figure 5.1-5

Begin by expressing 3x− 2 y=6inslope-intercept form.

3 x− 2 y= 6

− 2 y=− 3 x+ 6

y=

− 3

− 2

x+

6

− 2

y=

3

2

x− 3

Therefore, the slope of the line 3x− 2 y=6ism=

3

2

, and the slope of the line parallel to

the line 3x− 2 y=6 is also

3

2

. Since the line parallel to 3x− 2 y=6 passes through the point

(−1, 3), you can use the point-slope form to obtain the equationy− 3 =

3

2

(x−(−1)) or

y− 3 =

3

2

(x+1).

Example 2

Write an equation of the perpendicular bisector of the line segment joining the points

A(3, 0) andB(−1, 4). (See Figure 5.1-6.)