Section 3.2 Graphing Linear Equations 209 SECTION 3.2 Graphing Linear Equations ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Identify a linear equation in two variables. 2. Plot points to graph a linear equation in two variables. 3. Use intercepts to graph linear equations in two variables. 4. Recognize and graph horizontal and vertical lines. 5. Solve application problems. 6. Troubleshoot common errors. Objective 1 ▶ Identify a linear equation in two variables. The median annual income for men with a bachelor’s degree is given by the linear equation y = 1443x + 38,843, where x is the number of years after 1990. In this section, we will graph this equation and use the equation to find important information. Linear Equations in Two Variables In Chapter 2, we defined a linear equation in one variable as an equation of the form Ax + B = C, where A, B, and C are real numbers. The defining characteristic is that the exponent of the variable is 1. A linear equation in two variables is defined in a similar manner. Definition: An equation of the form Ax + By = C, where A, B, and C are real numbers with A and B not both zero is a linear equation in two variables. Note: The exponent of the variables x and y is 1. When the values of A, B, and C are integer values with A > 0, the linear equation is considered to be written in the standard form of a line, or Ax + By = C. Some examples of linear equations in two variables are y = 2x - 1 x 4 + 7y = 1 3x - 5y = 15 x + 4y = -8 (standard form) (standard form) The last two equations are written in standard form, while the first two are not. Objective 1 Examples Determine if the equation is a linear equation in two variables. If the equation is a linear equation in two variables, write it in standard form and identify the values of A, B, and C. 1a. x - y = 6 1b. y = 3 1c. 3x2 + y = 9 1d. y = 3 2 x - 2 Solutions 1a. This equation is a linear equation in two variables because the exponents of the variables are 1. It is also written in standard form. x - y = 6 1x + (-1) y = 6 A = 1, B = -1, C = 6 1b. This equation is a linear equation in two variables. The term with x is missing, so it is understood to have a coefficient of 0. y = 3 0x + 1y = 3 A = 0, B = 1, C = 3 Note: It is not necessary to write the coefficients of 0 or 1. They are written here for emphasis.
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