Graphing IntegersGraphing on the coordinate plane is a way to visualize relationships between two quantities. René Descartes was the French mathematician and philosopher who discovered this unique way to combine algebra and geometry. He recognized that by drawing two perpendicular number lines called axes, and labeling them with positive and negative numbers, he could locate any point on the plane with x and ycoordinates. The diagram below shows the different parts of the coordinate plane
The point where the xaxis and yaxis intersect is called the origin. Notice that xvalues to the right of the yaxis are positive and xvalues to the left of the yaxis are negative. Similarly, yvalues above the xaxis are positive and yvalues below the xaxis are negative. The axes divide the plane into four quadrants which are numbered starting in the upper right hand quadrant going counterclockwise as I, II, III, and IV.
An ordered pair of numbers is used to locate any point on the plane. An ordered pair is enclosed in a pair of parentheses with the first number representing a location on the xaxis, the xcoordinate, and the second number representing a location on the yaxis, the ycoordinate. To locate a point on the coordinate plane, do the following:
Look at the coordinate grid below. The ordered pair for point A is (3, 2). To locate point A , we move three units to the right and two units down. Also shown on the coordinate plane are points B (3, 5), C (1, 4), D (0, 3), E (2,4) and F (4,0).
Notice that points in quadrant I have both a positive x and ycoordinate. Points in quadrant II have a negative xcoordinate and a positive ycoordinate. Points in quadrant III have both a negative x and ycoordinate, and points in quadrant IV have a positive xcoordinate and a negative ycoordinate. One way to represent relationships between pairs of numbers is through the use of an equation like x – 2 = y. A second way to represent that same relationship is through the use of a function table like the one below.
This table can then be used to create the graph of the relationship. By plotting the points from the table above, we can see the relationship which exists between the points which satisfy the equation x – 2 = y.
We can now see that the pattern of dots lies along a straight line. By connecting the dots with a solid line and indicating that it can be extended in both directions, we have the graph of x – 2 = y. A linear function is one which when graphed becomes a straight line. 

