Graph.

Graph. Graph, a diagram that shows relationships between numbers. Graphs arrange numerical information into a picture from which it is often possible to see overall patterns or trends in the information. The graph in figure 1 illustrates a sales trend. It shows the number of glasses of lemonade sold each day for a week. To find the number of glasses sold on day 3, first locate the number 3 on the horizontal axis and then find the point directly above it. The position of this point corresponding to the vertical axis is 10, meaning that 10 glasses were sold on day 3. On day 1, the number of glasses sold is hard to determine precisely, but is somewhere between 15 and 20. Though this graph, like most graphs, is not as accurate as a list of numbers, it more clearly illustrates the overall trend that lemonade sells better toward the end of the week (days 6 and 7) than in the middle of the week. The graph in figure 2 illustrates numerical relationships. Suppose it is known that Yolanda is four years older than Xavier. Using y for Yolanda's age and x for Xavier's age, this relationship can be written as y = x + 4. Since 5 = 1 + 4, one possible pair of values for x and y is x = 1 and y = 5, which can be written briefly as (1,5) (see Coordinate System). The set of all the pairs (x,y) for which y = x + 4 is represented by the blue straight line plotted in figure 2. Graphs can be used to solve equations simultaneously. Suppose that in addition to knowing that Yolanda is four years older than Xavier, it is also known that Yolanda is three times Xavier's age. The problem, then, is to find values for x and y that make the equations y = x + 4 and y = 3x both true at the same time. In figure 2, these two equations are plotted together; the solution of these simultaneous equations is the point at which the two graphs intersect (2,6), which shows that Xavier is two years old and Yolanda is six years old. Graphs can also be used to exhibit inequalities. The curve in figure 3 graphs the parabolay = x2 - 1. The shaded area, not including this curve, is the graph of the inequality y>x2 - 1. Contributed By: William James Ralph Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.