Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Quadratic Equations And Polynomials
Introduction: Maps and Graphs
Before modern GPS, mapmakers used latitude and longitude to pinpoint locations. San Francisco, for example, lies at 37° north latitude and 122° west longitude. Every location on Earth has a unique pair of coordinates.
In mathematics, the Cartesian plane serves as a map. Instead of latitude and longitude, we use x and y coordinates. Every point has a unique ordered pair (x, y).
The Cartesian Plane
The Cartesian plane consists of two perpendicular number lines:
| Axis | Description | | x-axis | Horizontal line (like the equator) | | y-axis | Vertical line (like the prime meridian) | | Origin | The point (0,0) where the axes intersect |
Ordered Pairs
An ordered pair (x, y) specifies a point's location:
- The first number (x) indicates horizontal position (positive = right, negative = left)
- The second number (y) indicates vertical position (positive = up, negative = down)