6.6 Graphing Linear Equations 341 y 4 5 6 3 2 1 21 22 23 24 2423 25 1 2 3 4 5 x y 5 x 1 1 (–3, –2) (1, 2) (2, 3) (3, 4) (4.5, 5.5) 2221 Figure 6.7 All equations of the form ax by c a b , 0 and 0, + = ≠ ≠ will be straight lines when graphed. Thus, such equations are called linear equations in two variables . The exponents on the variables x and y must be 1 for the equation to be linear. Since only two points are needed to draw a line, only two points are needed to graph a linear equation. However, it is always a good idea to plot a third point as a checkpoint. If no error has been made, all three points will be in a line, or collinear . One method that can be used to obtain points is to solve the equation for y, substitute values for x, and determine the corresponding values of y. Learning Catalytics Keyword: Angel-SOM-6.6 (See Preface for additional details.) Example 3 Graphing an Equation by Plotting Points Graph y x2 2. = + Solution Since the equation is already solved for y, select values for x and determine the corresponding values for y. The table below indicates values arbitrarily selected for x and their corresponding values for y. The ordered pairs are (0, 2), (1, 4), and ( 1, 0). − The graph is shown in Fig. 6.8. x y 0 2 1 4 1− 0 Now try Exercise 45 21 22 23 24 25 y x 22 23 24 25 1 2 3 4 5 2 3 4 5 6 7 (21, 0) (0, 2) (1, 4) x-intercept y-intercept y 5 2x 1 2 1 21 Figure 6.8 7 GRAPHING LINEAR EQUATIONS BY PLOTTING POINTS 1. Solve the equation for y. 2. Select at least three values for x and determine their corresponding values of y. 3. Plot the points. 4. The points should be in a straight line. Draw a line through the set of points and place arrow tips at both ends of the line. PROCEDURE MATHEMATICS TODAY Use of Grids Grids have long been used in mapping. In archaeological digs, a rectangular coordinate system may be used to chart the location of each find. Why This Is Important Grids form the basis for plotting points when graphing equations, and also for locating cities and streets on maps. Tom Uhlman/Alamy Stock Photo
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