128 Chapter 2 Linear Equations in Two Variables and Functions Section 2.1 Linear Equations in Two Variables Table 2-1 Percentage of Individuals Who Participate in Leisure Sports Activities Versus Age 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 Percent Age of Participant (years) In this example, two variables are related: age and the percentage of individuals who participate in leisure sports activities. To picture two variables simultaneously,we use a graph with two number lines drawn at right angles to each other (Figure 2-2). This forms a rectangular coordinate system.The horizontal line is called the x-axis, and the vertical line is called the y-axis.The point where the lines intersect is called the origin. On the x-axis, the numbers to the right of the origin are positive, and the numbers to the left are negative.On the y-axis, the numbers above the origin are positive, and the numbers below are negative.The x- and y-axes divide the graphing area into four regions called quadrants. Concepts 1. The Rectangular Coordinate System 2. Linear Equations in Two Variables 3. Graphing Linear Equations in Two Variables 4. x- and y-Intercepts 5. Horizontal and Vertical Lines 1. The Rectangular Coordinate System One application of algebra is the graphical representation of numerical information (or data). For example,Table 2-1 shows the percentage of individuals who participate in leisure sports activities according to the age of the individual. Percentage of Individuals Age Participating in Leisure (years) Sports Activities 20 59% 30 52% 40 44% 50 34% 60 21% 70 18% Source: U.S. National Endowment for the Arts Information in table form is difficult to picture and interpret.However, when the data are presented in a graph, there appears to be a downward trend in the participation in leisure sports activities as age increases (Figure 2-1). Figure 2-1 6 5 4 3 2 1 Origin 21 6 6543 0 1 2 3 4 5 1 2 3 4 5 6 y-axis x-axis Quadrant II Quadrant I Quadrant III Quadrant IV Figure 2-2
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