1 Plot Ordered Pairs The Cartesian coordinate system has a horizontal number line, called the x-axis, and a vertical number line, called the y-axis. (See Figure 2.) The x-axis and y-axis determine a fl at surface called a plane. The axes divide this plane into four quadrants. The point at which the x-axis and y-axis intersect is called the origin. The arrow at one end of the x-axis and one end of the y-axis indicates the positive direction on each axis. Each point in the plane is represented by an ordered pair of real numbers (x, y). The fi rst number in the ordered pair is called the x-coordinate (also called the abscissa), and it tells us the distance and direction of the point from the origin along the x-axis. The second number in the ordered pair is the y-coordinate (also called the ordinate), and it tells us the distance and direction of the point from the origin either on the y-axis or parallel to the y-axis. The origin has coordinates (0, 0). Amount Spent Online for Consumer Electronics 2001 2002 2003 2004 2005 2006 2007 Year Dollars (in billions) 9 8 7 6 5 4 3 2 1 Figure 1 (www.census.gov) x y y-axis Quadrant I Origin (0, 0) x-axis Quadrant II Quadrant III Quadrant IV x y (4, 2) Right 4 Up 2 5 5 5 5 Figure 2 Figure 3 Notice that from quadrant I, we move counterclockwise to move through the quadrants in order. Beginning at the origin, notice that we first move horizontally, then move vertically to plot points. We have graphed the ordered pair (4, 2) on the coordinate system in Figure 3. This is also called plotting the point (4, 2). The x-coordinate of the point is 4. It tells us to move 4 units to the right from the origin along the x-axis. The y-coordinate of the point is 2. From the current position, move 2 units up, parallel to the y-axis. We can use ordered pairs to represent the points on the line graph in Figure 1 just like we use them to represent points in the Cartesian coordinate system. In Figure 1, the years are on the horizontal axis, and the amount of money spent online on consumer electronics is on the vertical axis. If we move along the horizontal axis to the year 2005 and then move up, parallel to the vertical axis, we fi nd the billions of dollars spent shopping online for consumer electronics during that year. This point can be represented by the ordered pair (2005, 4.7), and it tells us that in 2005 shoppers spent approximately $4.7 billion online on consumer electronics. 140 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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