Geometry: An Interactive Journey to Mastery

Lesson 11: Making Use of Linear Equations

Solution

Such a line has slope ^5624  16 and, therefore, has equation yx 64.^16

The xLQWHUFHSWRIWKHOLQHLVWKHSRLQWDWZKLFKWKHOLQHFURVVHVWKHxD[LV:HKDYHy = 0 at this point.

Substituting and solving gives

06164

32.

x

x

 



The xLQWHUFHSWLVͼ௘í௘ͽ

The yLQWHUFHSWLVWKHSRLQWDWZKLFKWKHOLQHFURVVHVWKHyD[LV²WKDWLVWKHORFDWLRQDWZKLFKx = 0. Substituting

and solving gives

(^60416)

5.^13

y

y

 

The yLQWHUFHSWLV§· ̈ ̧©¹0, 5^13.

Example 3

What is the slope of the line shown in Figure 11.4? Name a point this line

passes through. Quickly write the equation of the line.

Solution

The line has slope ^23 DQGSDVVHVWKURXJKWKHSRLQWͼ௘௘ͽ,WKDVHTXDWLRQyx 2.^23

ͼ௘$OWHUQDWLYHO\QRWLQJWKDWWKHOLQHSDVVHVWKURXJKͼ௘௘ͽZHFRXOGDOVRZULWHWKHHTXDWLRQRIWKHOLQHDV

yx  ^23 3.௘ͽ

Example 4

Write an equation for the perpendicular bisector of PQ, where P ͼ௘௘ͽDQGQ ͼ௘௘ͽ

3

y

2

x

Figure 11.4