This chapter covers graphing functions and linear equations using various types of graphing systems.

EO 1.8

STATE the definition of the following terms: a. Ordinate

b. Abscissa

EO 1.9Given a table of data, PLOT the data points cartesian coordinate graph.

on a

EO 1.10 Given a table of data, PLOT the data points logarithmic coordinate graph.

on a

EO 1.11 Given a table of data, PLOT the data points on the appropriate graphing system to obtain the specified curve.

EO 1.12 EO 1.13

Obtain data from a given graph.

Given the data, SOLVE for the unknown using a nomograph.

In work with physical systems, the relationship of one physical quantity to another is often of interest. For example, the power level of a nuclear reactor can be measured at any given time. However, this power level changes with time and is often monitored. One method of relating one physical quantity to another is to tabulate measurements. Thus, the power level of a nuclear reactor at specific times can be recorded in a log book. Although this method does provide information on the relationship between power level and time, it is a difficult method to use effectively. In particular, trends or changes are hard to visualize. Graphs often overcome these disadvantages. For this reason, graphs are widely used.

A graph is a pictorial representation of the relationship between two or more physical quantities. Graphs are used frequently both to present fundamental data on the behavior of physical systems and to monitor the operation of such systems. The basic principle of any graph is that distances are used to represent the magnitudes of numbers. The number line is the simplest type of graph. All numbers are represented as distances along the line. Positive numbers are located to the right of zero, and negative numbers are located to the left of zero.

The coordinate system of a graph is the framework upon which the graph is drawn. A coordinate system consists of numbered scales that give the base and the direction for measuring points on the graph. Any point on a graph can be specified by giving its coordinates. Coordinates describe the location of the point with respect to the scales of the coordinate system. There are several different coordinate systems commonly encountered.

The Cartesian Coordinate Svstem

The Cartesian Coordinate System, also known as the rectangular coordinate system, consists of two number scales, called the x-axis (at y = 0) and the y-axis (at x = 0), that are perpendicular to each other. Each scale is a number line drawn to intersect the other at zero. The zero point is called the origin. The divisions along the scales may be any size, but each division must be equal. Figure 1 shows a rectangular coordinate system. The axes divide the coordinate system into four regions called quadrants. Quadrant I is the region above the x-axis and to the right of the y-axis. Quadrant II is the region above the x-axis and to the left of the y-axis. Quadrant III is the region below the x-axis and to the left of the y-axis. Quadrant IV is the region below the x-axis and to the right of the y-axis.

Figure 1 The Cartesian System

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).