Various forms of equations of a line

Various Forms of Equations of a Line A line is a geometric object with an infinite length that has no width or thickness. It can be represented by various f...

Various Forms of Equations of a Line

A line is a geometric object with an infinite length that has no width or thickness. It can be represented by various forms, including linear equations, parametric equations, and polar coordinates.

Linear Equations:

A linear equation in the form of $Ax + By + C = 0$ represents a line where the variable x represents the independent variable and the variable y represents the dependent variable. The values of A, B, and C determine the slope and y-intercept of the line.

Parametric Equations:

A parametric equation in the form of $x = a + t$ and $y = b + t$ defines a line where t is the independent variable. Here, a and b are constants that determine the position of the point on the line for any given value of t.

Polar Coordinates:

In polar coordinates, the line is represented by the equation $r = a + b\theta$ , where a and b are constants. Here, r represents the radial distance from the origin, and θ is the angular position.

Summary:

A linear equation: $Ax + By + C = 0$
Parametric equations: $x = a + t$ and $y = b + t$
Polar coordinates: $r = a + b\theta$