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The word line may also refer, in everyday life, to a line segment, which is a part of a line delimited by two points (its endpoints). Euclid's Elements defines a straight line as a "breadthless length" that "lies evenly with respect to the points on itself", and introduced several postulates as basic unprovable properties on which the rest of ...
A general straight-line thread connects the two points (0, k−t) and (t, 0), where k is an arbitrary scaling constant, and the family of lines is generated by varying the parameter t. From simple geometry, the equation of this straight line is y = −(k − t)x/t + k − t. Rearranging and casting in the form F(x,y,t) = 0 gives:
Animation for Peaucellier–Lipkin linkage: Dimensions: Cyan Links = a Green Links = b Yellow Links = c. The Peaucellier–Lipkin linkage (or Peaucellier–Lipkin cell, or Peaucellier–Lipkin inversor), invented in 1864, was the first true planar straight line mechanism – the first planar linkage capable of transforming rotary motion into perfect straight-line motion, and vice versa.
The motion of a particle (a point-like object) along a line can be described by its position , which varies with (time). An example of linear motion is an athlete running a 100-meter dash along a straight track. [2] Linear motion is the most basic of all motion.
These points form a line, and y = x is said to be the equation for this line. In general, linear equations involving x and y specify lines, quadratic equations specify conic sections, and more complicated equations describe more complicated figures. [17] Usually, a single equation corresponds to a curve on the plane.
A straight-line mechanism is a mechanism that converts any type of rotary or angular motion to perfect or near-perfect straight-line motion, or vice versa. Straight-line motion is linear motion of definite length or "stroke", every forward stroke being followed by a return stroke, giving reciprocating motion. The first such mechanism, patented ...
[1]: p. 23 From this, every straight line has a linear equation homogeneous in x, y, z. Every equation of the form l x + m y + n z = 0 {\displaystyle lx+my+nz=0} in real coefficients is a real straight line of finite points unless l : m : n is proportional to a : b : c , the side lengths, in which case we have the locus of points at infinity.
Vertical line of equation x = a Horizontal line of equation y = b. Each solution (x, y) of a linear equation + + = may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that a and b are not both zero. Conversely, every line is the set of all ...