Chapter 4: Summary Definition/Procedure Example 4.1 Introduction to Linear Equations in Two Variables www.mhhe.com/messersmith x 5 5 5 x 4 5 12 (4, 2) (2, 3) (0, 4) x y 0 4 2 3 4 2 A linear equation in two variables can be written in the form Ax By C where A, B, and C are real numbers and where both A and B do not equal zero. To determine whether an ordered pair is a solution of an equation, substitute the values for the variables. (p. 142) Graphing by Plotting Points and Finding Intercepts The graph of a linear equation in two variables, Ax By C, is a straight line. Each point on the line is a solution to the equation. We can graph the line by plotting the points and drawing the line through them. (p. 143) Is (5, 3) a solution of 2x 7y 31? Substitute 5 for x and 3 for y. 2x 7y 31 2(5) 7(3) 31 10 (21) 31 10 21 31 31 31 True Yes, (5, 3) is a solution. Graph y 1 2 x 4 by plotting points. Make a table of values. Plot the points, and draw a line through them. The x-intercept of an equation is the point where the graph intersects the x-axis. To fi nd the x-intercept of the graph of an equation, let y 0 and solve for x. The y-intercept of an equation is the point where the graph intersects the y-axis. To fi nd the y-intercept of the graph of an equation, let x 0 and solve for y. (p. 144) Graph 5x 2y 10 by fi nding the intercepts and another point on the line. x-intercept: Let y 0 and solve for x. 5x 2(0) 10 5x 10 x 2 The x-intercept is (2, 0). y-intercept: Let x 0, and solve for y. 5x 2y 10 5(0) 2y 10 2y 10 y 5 The y-intercept is (0, 5). Another point on the line is (4, 5). Plot the points, and draw the line through them. x y 5 5 5x 2y 1 5 5 5 2 5 CHAPTER 4 Summary 215
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