The Cartesian Coordinate System: Linear Inequations
Aaron Griffin
Math 4091A
March 17, 2015
The Cartesian Coordinate System
Linear inequalities (statements such as “4≤X+10<18”) can be represented graphically along a number line. In similar manner, a linear equation in two variables (this being the form ax+by=c) can also be represented graphically, using two axes; the x axis, the horizontal plane, and the y axis, the vertical plane.
There are memory tricks with which to distinguish the x from the y axis and remember their horizontal and vertical orientations.
Regarding the x axis and its horizontal orientation, keep in mind that the word “horizontal” is derived from the word “horizon”. The horizon line at limit of vision when viewing the ocean, or an open field, lies from left to right, just as the horizontal x axis lies from left to right along the coordinate plane. Another way to remember that the x axis is horizontal is to imagine the letter “x” as a deer viewed from the front with splayed legs and long antlers. Imagining the horizontal x axis as the ground on a two dimensional plane, the deer would walk along the x axis from right to left. …show more content…
The letter “y” can be likened to a shape of a bird in flight, able to rise or descend up or down, just the “y” axis is oriented perpendicular to the x axis, going “up and down” upon the two dimensional plane.
Linear equations in two variables feature not a single solution, but a specifically defined solution set, within which they are infinite possibilities. These solution sets can be represented graphically using the dual axis system of coordinates, on which these solution sets are graphed as lines.
This system is commonly known as the Cartesian coordinate system, or the “Cartesian plane”, after the 17th century mathematician and philosopher René Descartes who first developed
Math 4091A
March 17, 2015
The Cartesian Coordinate System
Linear inequalities (statements such as “4≤X+10<18”) can be represented graphically along a number line. In similar manner, a linear equation in two variables (this being the form ax+by=c) can also be represented graphically, using two axes; the x axis, the horizontal plane, and the y axis, the vertical plane.
There are memory tricks with which to distinguish the x from the y axis and remember their horizontal and vertical orientations.
Regarding the x axis and its horizontal orientation, keep in mind that the word “horizontal” is derived from the word “horizon”. The horizon line at limit of vision when viewing the ocean, or an open field, lies from left to right, just as the horizontal x axis lies from left to right along the coordinate plane. Another way to remember that the x axis is horizontal is to imagine the letter “x” as a deer viewed from the front with splayed legs and long antlers. Imagining the horizontal x axis as the ground on a two dimensional plane, the deer would walk along the x axis from right to left. …show more content…
The letter “y” can be likened to a shape of a bird in flight, able to rise or descend up or down, just the “y” axis is oriented perpendicular to the x axis, going “up and down” upon the two dimensional plane.
Linear equations in two variables feature not a single solution, but a specifically defined solution set, within which they are infinite possibilities. These solution sets can be represented graphically using the dual axis system of coordinates, on which these solution sets are graphed as lines.
This system is commonly known as the Cartesian coordinate system, or the “Cartesian plane”, after the 17th century mathematician and philosopher René Descartes who first developed