## 1.2 Lines in the Plane

### Summary

A line is one of the most important geometric objects for representing points in the plane. We shall also see later that, much like the experience we have when zooming in, many curves in the plane are approximately linear in small regions. In this section we learn how to recognize a line from its equation, and we learn how to write the equation of a line from information about it.

By the end of your studying, you should know:

• The definition of slope.
• The point-slope form of the equation of a line.
• The slope-intercept form of the equation of a line.
• The relationship between the slopes of parallel lines.
• The relationship between the slopes of perpendicular lines.

On-screen applet instructions: Move the sliders and describe the effect.

### Examples

Let L1 be the line ax + by = c, where a, b, and c are constants. What is the equation of the line perpendicular to L1, passing through the point (0, c)?

Find the equation of a line through (1, 1) perpendicular to a line passing through (1, 2) and (3, 5).

Consider a triangle with vertices (1, 1), (9, 7), and (3, 11). Do the perpendicular bisectors of the sides of the triangle intersect in a single point?

### Videos

See short videos of worked problems for this section.

### Exercises

See Exercises for 1.2 Lines in the Plane (PDF).

Work online to solve the exercises for this section, or for any other section of the textbook.

### Resources on the Web

Information on Newton
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"

Calculus Applications
Project Intermath

Plane Division by Lines
Wolfram Research

#### Interesting Application

Do you see lines in the waves?

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel