Before the end of the European Renaissance, math was cleanly divided into the two separate subjects of geometry and algebra. You didn't use algebraic equations in geometry, and you didn't draw any pictures in algebra. Then, around 1637, a French guy named René Descartes (pronounced "ray-NAY day-CART") came up with a way to put these two subjects together.
Rene Descartes was born on March 31, 1596, in Touraine, France. He was entered into Jesuit College at the age of eight, where he studied for about eight years. Although he studied the classics, logic and philosophy, Descartes only found mathematics to be satisfactory in reaching the truth of the science of nature. He then received a law degree in 1616. Thereafter, Descartes chose to join the army and served from 1617-1621. Descartes resigned from the army and traveled extensively for five years. During this period, he continued studying pure mathematics.
Finally, in 1628, he devoted his life to seeking the truth about the science of nature. At that point, he moved to Holland and remained there for twenty years, dedicating his time to philosophy and mathematics. During this time, Descartes had his work "Meditations on First Philosophy" published. It was in this work that he introduced the famous phrase "I think, therefore I am." Descartes hoped to use this statement to find truth by the use of reason. He sought to take complex ideas and break them down into simpler ones that were clear. Descartes believed that mathematics was the only thing that is certain or true. Therefore, it could be used to reason the complex ideas of the universe into simpler ideas that were true. In 1638, La Geometrie was published. This work was responsible for making Descartes famous in mathematics history, because it was the invention of analytical geometry. Analytical geometry is basically applying algebra to geometry. Descartes introduced this theory about determining a point in a plane by pairs of real numbers (ordered pairs). This is known as the Cartesian Plane.
Now let’s explore:
You learned about the basic (counting) number line back in elementary school: Later on, you were introduced to zero and negatives, which completed the number line:

Descartes' breakthrough was in taking a second number line, standing it up on its end, and crossing the first number line at zero: The Cartesian plane consists of two directed lines that perpendicularly intersect their respective zero points. The horizontal line is called the x-axis and the vertical line is called the y-axis. The point of intersection of the x-axis and the y-axis is called the origin and is denoted by the letter O. The arrows at the ends of the axes indicate the direction in which the numbers are getting larger. Therefore, only the axes should have arrows. The whole flat expanse, top to bottom, side to side, bursting outside, (see below), and stretching off to infinity in all directions, is called the "plane". When you put the two axes in the plane, it is then called the "Cartesian" ("carr-TEE-zhun") plane.

The position of any point on the Cartesian plane is described by using two numbers: (x, y). The first number, x, is the horizontal position of the point from the origin. It is called the x-coordinate. The second number, y, is the vertical position of the point from the origin. It is called the y-coordinate. Since a specific order is used to represent the coordinates, they are called ordered pairs. For example, the ordered pair (5, 8) represents a point 5 units to the right of the origin in the direction of the x-axis and 8 units above the origin in the direction of the y-axis as shown in the diagram above. The two axes divide the plane into four sections called "quadrants". The quadrants are labeled with Roman numerals, starting at the positive x-axis and going around anti-clockwise, also noted above in green. It was this work that made Rene Descartes very instrumental to the history of mathematics. Since its inception, the system of coordinates is used in many modern applications. For example, on any map the location of a country or a city is usually given as a set of coordinates. The location of a ship at sea is determined by longitude and latitude, which is an application of the coordinate system. Computer graphic artists create figures and computer animation by referencing coordinates on the screen. Indeed, Rene Descartes was one of the most important and influential thinkers in history.

Works cited
1. Barile, Margherita. "Cartesian Plane." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/CartesianPlane.html
2. Burton, David. The History of Mathematics: An Introduction. New York: Allyn and Bacon, 1985.
3. Latham, M. L. and Smith, D. E. The Geometry of René Descartes, with a Facsimile of the First Edition, 1637. La Salle, IL: Open Court, 1952.