Section 3.2 Linear Equations in Two Variables 203 Expanding Your Skills 31. The data in the table give the percent of males and females who have completed 4 or more years of college education for selected years. Let x represent the number of years since 1960. Let y represent the percent of men and the percent of women that completed 4 or more years of college. a. Plot the data points for men and for women on the same graph. b. Is the percentage of men with 4 or more years of college increasing or decreasing? c. Is the percentage of women with 4 or more years of college increasing or decreasing? 32. Use the data and graph from Exercise 31 to answer the questions. a. In which year was the difference in percentages between men and women with 4 or more years of college the greatest? 35 30 25 20 15 10 5 y 0 0 5 10 15 20 25 30 35 40 45 Year (x 5 0 corresponds to 1960) b. In which year was the difference in percentages between men and women the least? c. If the trend continues beyond the data in the graph, does it seem possible that in the future, the percentage of women with 4 or more years of college will be greater than or equal to the percentage of men? 50 x Percent of Males/Females with 4 or More Years of College, United States Percent Linear Equations in Two Variables Section 3.2 1. Definition of a Linear Equation in Two Variables Concepts Recall that an equation in the form where is called a linear 1. Definition of a Linear equation in one variable.A solution to such an equation is a value of x that makes the equation a true statement. For example, has a solution of Equation in Two Variables 2. Graphing Linear Equations in Two Variables by Plotting Points 3. x- and y-Intercepts 4. Horizontal and Vertical Lines ax b c, a 0, 3x 5 1 2. In this section, we will look at linear equations in two variables. Linear Equation in Two Variables Let A, B, and C be real numbers such that A and B are not both zero.Then, an equation that can be written in the form: Ax By C is called a linear equation in two variables. Percent, y Percent, y Year x Men Women 1960 0 9.7 5.8 1970 10 13.5 8.1 1980 20 20.1 12.8 1990 30 24.4 18.4 2000 40 27.8 23.6 2005 45 28.9 26.5 2010 50 29.9 28.8
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