Line
In mathematics, a line is a basic geometric object that extends infinitely in both directions
In mathematics, a line is a basic geometric object that extends infinitely in both directions. It is often represented by a straight, thin, and infinitely long path. A line has a constant slope and is characterized by two properties:
1. Length: Unlike a line segment, which has a finite length defined by its two endpoints, a line has infinite length. This means it extends indefinitely in both directions.
2. Direction: A line has a constant slope, which determines its direction. The slope refers to the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. It can be positive, negative, zero, or undefined.
A line can be defined in different ways:
1. Slope-intercept form: This is a commonly used equation of a line in the form y = mx + b, where m represents the slope, and b represents the y-intercept (the point where the line intersects the y-axis).
2. Point-slope form: Another equation of a line is y – y₁ = m(x – x₁), where (x₁, y₁) represents a point on the line, and m represents the slope.
3. Two-point form: An equation can be formed from two points (x₁, y₁) and (x₂, y₂) on the line as (y – y₁)/(y₂ – y₁) = (x – x₁)/(x₂ – x₁).
Lines are important in various areas of mathematics, including geometry, algebra, and calculus. They are widely used to represent relationships between quantities, describe motion, and solve problems involving equations and linear equations.
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