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Horizontal and vertical lines. In the general equation of a line, ax + by + c = 0, a and b cannot both be zero unless c is also zero, in which case the equation does not define a line. If a = 0 and b ≠ 0, the line is horizontal and has equation y = -c/b.
The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2x) A curve intersecting an asymptote infinitely many times In analytic geometry , an asymptote ( / ˈ æ s ɪ m p t oʊ t / ) of a curve is a line such that the distance between the curve and the line approaches zero as one or ...
Gradients are expressed as a ratio of vertical rise to horizontal distance; for example, a 1% gradient (1 in 100) means the track rises 1 vertical unit for every 100 horizontal units. On such a gradient, a locomotive can pull half (or less) of the load that it can pull on level track.
This can be seen by applying the Pythagorean theorem to a right triangle with horizontal and vertical sides, having the line segment from to as its hypotenuse. The two squared formulas inside the square root give the areas of squares on the horizontal and vertical sides, and the outer square root converts the area of the square on the ...
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
Lines may not only be drawn 8-connected, but also 4-connected, meaning that only horizontal and vertical steps are allowed, while diagonal steps are prohibited. Given a raster of square pixels, this leads to every square containing a part of the line being colored.
Variations of the horizontal line test can be used to determine whether a function is surjective or bijective: The function f is surjective (i.e., onto) if and only if its graph intersects any horizontal line at least once. f is bijective if and only if any horizontal line will intersect the graph exactly once.
The word horizontal is derived from the Latin horizon, which derives from the Greek ὁρῐ́ζων, meaning 'separating' or 'marking a boundary'. [2] The word vertical is derived from the late Latin verticalis, which is from the same root as vertex, meaning 'highest point' or more literally the 'turning point' such as in a whirlpool.