Connectivity in Graphs by W. T. Tutte

By W. T. Tutte

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1 y = x - 1 2 1 x + y = 2 3 65. y = 2x + 3 66. y = - 3x + 4 67. 69. 2x - 3y = 6 70. 3x + 2y = 6 71. x + y = 1 72. x - y = 2 73. x = - 4 74. y = - 1 75. y = 5 76. x = 2 77. y - x = 0 78. x + y = 0 79. 2y - 3x = 0 80. 3x + 2y = 0 68. In Problems 81–88, use a graphing utility to graph each linear equation. Be sure to use a viewing rectangle that shows the intercepts. Then locate each intercept rounded to two decimal places. 81. 8y = 2 85. 82. 7y = 8 4 6 2 x + y = 17 23 3 86. 9 3 2 x - y = 14 8 7 83.

A) Assuming that the dollar amount of annual increase in net revenue will remain constant, find a linear equation expressing net revenue R for Dell, Inc. Let t = 0 correspond to the fiscal year ending in 2008. (b) Use the equation found in part (a) to predict the net revenue for Dell, Inc. for the fiscal year ending in 2011. Source: Dell, Inc. 1 Lines 21 117. Cost of Gasoline The average price of a gallon of regular 118. 847. Suppose that the Smith family drives a 2010 GMC Yukon 1500 4WD, which has a fuel usage of 17 miles per gallon (city and highway combined).

SOLUTION FIGURE 20 y The slope of a horizontal line is 0. To get an equation, we use the point–slope form with m = 0, x1 = 3, and y1 = 2: y - y1 y - 2 y - 2 y 5 3 (3, 2) y = 2 1 –1 x 1 3 5 = = = = m(x - x1) 0 # (x - 3) 0 2 Point–slope form m = 0, x1 = 3, y1 = 2 ■ See Figure 20 for the graph. As suggested by Example 10, we have the following result: ▲ Theorem Equation of a Horizontal Line A horizontal line is given by an equation of the form y‫؍‬b where (0, b) is the y-intercept. NOW WORK PROBLEM 17(b).

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