Cartesian Coordinate Graphs

Figure 2 Cartesian Coordinate Graph of Temperature vs. Time

Mathematics Volume 1 of 2
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GRAPHING Algebra The use of a graph starts with the plotting of data points using the coordinate system. These data points are known as the abscissa and the ordinate. The abscissa, also known as the y-coordinate, is the distance along the y-axis. The ordinate, also known as the x-coordinate, is the distance along the x-axis. A point on a Cartesian coordinate graph is specified by giving its x-coordinate and its y-coordinate. Positive values of the x-coordinate are measured to the right, negative values to the left. Positive values of the y-coordinate are measured up, negative values down. For example, the x- and y-coordinates are both zero at the origin. The origin is denoted as (0,0), where the first zero refers to the value of the x-coordinate. Point A in Figure 1 is denoted as (0,4), since the value of the x-coordinate is zero, and the value of the y-coordinate is 4. In Quadrant I, every point has a positive x-coordinate and a positive y-coordinate. Point B in Figure 1 is located in Quadrant I and is denoted by (4,2). Fractional values of coordinates can also be shown. Point C in Figure 1 is denoted by (1,1.5). In Quadrant II, every point has a negative x-coordinate and a positive y-coordinate. Point D is denoted by (-2,2). In Quadrant III, every point has a negative x-coordinate and a negative y-coordinate. Point E is located in Quadrant III and is denoted by (-2,-4). In Quadrant IV, every point has a positive x-coordinate, but a negative y-coordinate. Point F is located in Quadrant IV and is denoted by (5,-4). Cartesian Coordinate Graphs The most common type of graph using the Cartesian Coordinate System is one in which all values of both the x-coordinate and the y-coordinate are positive. This corresponds to Quadrant I of a Cartesian coordinate graph. The relationship between two physical quantities is often shown on this type of rectangular plot. The x-axis and the y-axis must first be labeled to correspond to one of the physical quantities. The units of measurement along each axis must also be established. For example, to show the relationship between reactor power level and time, the x-axis can be used for time in minutes and the y-axis for the reactor power level as a percentage of full power level. Data points are plotted using the associated values of the two physical quantities. Example: The temperature of water flowing in a high pressure line was measured at regular intervals. Plot the following recorded data on a Cartesian coordinate graph. Time (min) Temperature (°F) 0 400° 15 420° 30 440° 45 460° 60 480° 75 497° 90 497° 105 497° 120 497° MA-02 Page 74 Rev. 0

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