The idea of lines that join points of equal value was rediscovered several times. Įdmond Halley's New and Correct Chart Shewing the Variations of the Compass (1701) In the latter case, the method of interpolation affects the reliability of individual isolines and their portrayal of slope, pits and peaks. Contour lines may be either traced on a visible three-dimensional model of the surface, as when a photogrammetrist viewing a stereo-model plots elevation contours, or interpolated from the estimated surface elevations, as when a computer program threads contours through a network of observation points of area centroids.

The configuration of these contours allows map readers to infer the relative gradient of a parameter and estimate that parameter at specific places. A level set is a generalization of a contour line for functions of any number of variables.Ĭontour lines are curved, straight or a mixture of both lines on a map describing the intersection of a real or hypothetical surface with one or more horizontal planes. When the lines are close together the magnitude of the gradient is large: the variation is steep. The gradient of the function is always perpendicular to the contour lines. The contour interval of a contour map is the difference in elevation between successive contour lines. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. In cartography, a contour line (often just called a 'contour') joins points of equal elevation (height) above a given level, such as mean sea level. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value. It is a plane section of the three-dimensional graph of the function f ( x, y ) -plane.

If those slopes are equal, then the lines are found to be parallel.A two-dimensional contour graph of the three-dimensional surface in the above picture.Ī contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. Using those coordinate points, calculate the slope of each line. Two determine if two lines on a graph are parallel, first, find two coordinate points on each of the lines. In other words, the slopes of these lines are either equal or opposite.įor example, two lines both with the slope 3/4 would be parallel, but also a line with the slope 3/4 and the slope -3/-4 would also be parallel since even though they are headed in opposite directions, they would never cross paths when extended to infinity. Parallel lines are defined as any set of two or more lines that when extended to infinity, would never cross paths. X2 is any x coordinate on the parallel lineįrom these two equations, the slope-intercept form of the parallel line can be found and would equal:.y2 is any y coordinate on the parallel line.Where b is the y-intercept in the parallel line.Where m1 is the slope of the first line.The following formulas are used to calculate a parallel line.

Enter the slope-intercept form of the first equation, and a coordinate point the second line passes through to calculate the equation of the second line.

Parallel line equation calculator