Line

The line is a basic geometric shape. It is a straight, breadthless figure that extends to infinity in both directions and consists of infinitely many points strung all in a row with no spaces or breaks.

A line that can be drawn on paper is not actually a line, but a representation of a line since it does not extend infinitely in both directions. Two points determine a (unique) line which goes through them. A line can be broken down into finite line segments.

Common mathematical representations of a line include:

In two dimensions in the Cartesian plane:

• Standard Form: ax + by + c = 0
• Slope-Intercept Form: y = mx + b (where m is the slope of the line, b is the y-intercept)
• Point-Slope Form: (y - y₀) = m(x - x₀) (where m is the slope and (x₀, y₀) is a point on the line)
• Two Points Form: <math>(y - y_1) = \frac{y_2-y_1}{x_2-x_1}(x - x_1)</math> (where <math>(x_1,y_1)</math> and <math>(x_2,y_2)</math> are two different points on the line)

In n dimensions in Cartesian coordinates:

• Parametrized Vector Form: r(t) = <x₀, y₀,...> + t<x, y,...>

Philosophical nature of the line

The line is such an intuitive concept that most mathematicians think it escapes a formal, rigorous, and general definition. The definition above is unsatisfactory because adjectives such as "straight" are usually defined in terms of resembling lines. Other such intuitive concepts without rigorous definitions are the point, the plane, the set, symmetry, and infinity.

Attempts at providing a rigorous, abstract definition usually face philosophical paradoxes, such as Euclid's contention that lines are objects with "breadthless length." In other words, he asserted that a line in infinitely long, but has no width. Lines can also be considered as points strung together, or as curves with infinite radius of curvature, yet both these definitions have philosophical flaws as well. Airports See also: List of airports in Texas Texas has 730 airports, second most of any state in the nation. Largest in Texas by size and passengers served, Dallas/Fort Worth International Airport (DFW) is the second largest by area in the United States, and fourth in the world with 18,076 acres (73.15 km2).[298] In traffic, DFW is the busiest in the state, the fourth busiest in the United States,[299] and sixth worldwide.[300] American Airlines Group's American / American Eagle, the world's largest airline in total passengers-miles transported and passenger fleet size,[301] uses DFW as its largest and main hub. Southwest Airlines, headquartered in Dallas, has its operations at Dallas Love Field.[302] It ranks as the largest airline in the United States by number of passengers carried domestically per year and the largest airline in the world by number of passengers carried.[303] Texas's second-largest air facility is Houston's George Bush Intercontinental Airport (IAH). It served as the largest hub for the former Continental Airlines, which was based in Houston; it serves as the largest hub for United Airlines, the world's third-largest airline, by passenger-miles flown.[304][305] IAH offers service to the most Mexican destinations of any U.S. airport.[306][307] The next five largest airports in the state all serve over 3 million passengers annually; they include Austin-Bergstrom International Airport, William P. Hobby Airport, San Antonio International Airport, Dallas Love Field and El Paso International Airport. The smallest airport in the state to be designated an international airport is Del Rio International Airport.