Geometry: An Interactive Journey to Mastery

Example 1
Sketch graphs of the following lines.
D௘ͽ yí íͼ௘x௘ͽ
E௘ͽ y = 20x + 1.
F௘ͽ x = 3.
Solution
D௘ͽ yí íͼ௘xíͼ௘í௘ͽ௘ͽLVWKHHTXDWLRQRIDOLQHRIVORSH
íWKURXJKWKHSRLQWͼ௘í௘ͽ
 ͼ௘6HHFigure 11.1௘ͽ

E௘ͽ yí ͼ௘xí௘ͽLVDOLQHRIVORSHWKURXJKWKHSRLQWͼ௘௘ͽ

 ͼ௘6HHFigure 11.2௘ͽ

F௘ͽ $OOSRLQWVLQWKHSODQHZLWKxFRRUGLQDWHVDWLVI\x = 3,

so this is a vertical line.

 ͼ௘6HHFigure 11.3௘ͽ

Example 2
Find the xDQGyLQWHUFHSWVRIDOLQHWKDWSDVVHVWKURXJKWKHSRLQWVͼ௘௘ͽDQGͼ௘í௘ͽ

í 1

3

y

yí íͼxͽ

x

Figure 11.1

1

y

y = 20x + 1

x

Figure 11.2

3

y x = 3

x

Figure 11.3