Section 3.2 Linear Equations in Two Variables 211 5 y 2, x y 4 2 0 2 3 1 2 4 54 3 21 1 2 3 4 5 1 2 3 4 5 x 3 2 (2, 3) (2, 0) (2, 4) Answer 14. 5 4 3 2 1 y 54 3 21 1 2 3 5 1 2 3 4 5 x 4 x 4 Alternative Solution: Create a table of values for the equation The choice for the x-coordinate must be but y can be any real number. x must be 2. y can be any number. Skill Practice 14. Graph the equation. 3x 12 x 2. Topic: Graphing Linear Equations on an Appropriate Viewing Window Sometimes the standard viewing window does not provide an adequate display for the graph of an equation. For example, the graph of y x 15 is visible only in a small portion of the upper right corner of the standard viewing window. Calculator Connections A viewing window of a graphing calculator shows a portion of a rectangular coordinate system.The standard viewing window for many calculators shows the x-axis between and 10 and the y-axis between and 10 (Figure 3-13). Furthermore, the scale defined by the “tick” marks on both the x- and y-axes is usually set to 1. The “Standard Viewing Window” To graph an equation in x and y on a graphing calculator, the equation must be written with the y-variable isolated. For example, to graph the equation , we solve for y by applying the steps for solving a literal equation.The result, , can now be entered into a graphing calculator. To enter the equation , use parentheses around the fraction .The Graph option displays the graph of the line. 13 y 13 x 1 y 13 x 1 x 3y 3 10 10 Figure 3-13 TIP: Notice that a vertical line has an x-intercept but does not have a y-intercept (unless the vertical line is the y-axis itself ). To see where this line crosses the x- and y-axes, we can change the viewing window to accommodate larger values of x and y. Most calculators have a Range feature or Window feature that allows the user to change the minimum and maximum x- and y-values. To get a better picture of the equation y x 15, change the minimum x-value to 10 and the maximum x-value to 20. Similarly, use a minimum y-value of 10 and a maximum y-value of 20. Calculator Exercises For Exercises 1–8, graph the equations on the standard viewing window. 1. y 2x 5 2. y 3x 1
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