The most obvious is to plot relationships between one quantity and another. If for every thing you sell, you make 3 dollars, then you could express that as the equation y=3x and plot that using the Cartesian coordinate system. (where y would represent dollars and x would represent items sold)
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The cartesian coordinate system is the basic coordinate system people are familiar with. If you were to plot a basic X Y graph, where X and Y increase towards infinity, you are graphing in the cartesian coordinate system. There are a few other popular coordinate systems for more advanced math, but they are rarely used by most people. (polar coordinate system is common for some calculus equations)
A cartesian graph is a graph in which y is some function of x. This is the 'normal' type in which you can give an x and y coordinate. Other types include polar in which modulus is a function of argument, but there are loads of varieties and forms.
It is claimed thaht he got his inspiration while in bed - and watching a fly (or some bug) on the ceiling. He worked out that he could describe the bug's position on the ceiling using coordinates. And the rest, as they say, is history.
The reflection of a shape is defined with respect to some specified line. None is specified. If one were specified, the reflection of an object would be the set of points such that the line was exactly half-way between each point in the original shape and its reflection.
The word graph can be used either as a noun or a verb. As a noun, it means a picture or visualization of some mathematical term or relationship. The most usual type of graph is the Cartesian coordinate system invented by the great French mathematician, René Descartes, but there are several other types. As a verb, to graph is to depict in the form of a graph, as in, graph that equation.