Section 3.2 Linear Equations in Two Variables 221 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? Increasing c. Is the percentage of women with 4 or more years of college increasing or decreasing? Increasing 32. Use the data and graph from Exercise 31 to answer the questions. a. In which year was the difference in percentages between 35 30 25 20 15 10 5 y Percent of Males/Females with 4 or More Years of College, United States Males Females 0 0 5 10 15 20 25 30 35 40 45 50 Percent men and women with 4 or more years of college the greatest? 1980 Year (x 0 corresponds to 1960) b. In which year was the difference in percentages between men and women the least? 2010 c. If the trend continues beyond the data in the graph, does it seem possible that in the future, the x percentage of women with 4 or more years of college will be greater than or equal to the percentage of men? Yes Linear Equations in Two Variables Section 3.2 1. Definition of a Linear Equation in Two Variables Recall that an equation in the form ax b c, where a 0, is called 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, 3x 5 1 has a solution of 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. The equation x y 4 is a linear equation in two variables. A solution to such an equation is an ordered pair (x, y) that makes the equation a true statement. Several solutions to the equation x y 4 are listed here: Solution: Check: ✔ ✔ ✔ 1x, y2 x y 4 12, 22 122 122 4 11, 32 112 132 4 14, 02 142 102 4 11, 52 112 152 4 ✔ Concepts 1. Definition of a Linear Equation in Two Variables 2. Graphing Linear Equations in Two Variables by Plotting Points 3. x- and y-Intercepts 4. Horizontal and Vertical Lines Writing Translating Expression Geometry Scientific Calculator Video
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