1. Copyright © 2013 Pearson Education, Inc. Section 3.2 Linear Equations in Two Variables

2. Example Determine whether the given ordered pair is a solution to the given equation. a. y = x + 5, (2, 7) b. 2x + 3y = 18, (3,  4) Solution a. y = x + 5 7 = 2 + 5 7 = 7 True The ordered pair (2, 7) is a solution. Page 169

3. Example Determine whether the given ordered pair is a solution to the given equation. a. y = x + 5, (2, 7) b. 2x + 3y = 18, (3,  4) Solution b. 2x + 3y = 18 2(3) + 3(  4) = 18 6  12 = 18  6  18 The ordered pair (3,  4) is NOT a solution. Page 169

4. Example A table can be used to list solutions to an equation. Complete the table for the equation y = 3x – 1. Solution x 33 11 03 y Page 170

5. Find five solutions to the equation y = 3x + 2. Choose some x values and then compute the corresponding y values and complete the table. If x = -2, y = 3(-2) + 2 = -4. Ordered pair If x = -1, y = 3(-1) + 2 = -1. Ordered pair If x =0, y = 3(0) + 2 = 2. Ordered pair If x =1, y = 3(1) + 2 = 5. Ordered pair If x =2, y = 3(2) + 2 = 8. Ordered pair Graph on next slide. Finding Solutions of an Equation XY(x,y) -2 0 1 2 Page 170 A table that lists a few solutions is helpful when graphing an equation

6. Plot the five ordered pairs to obtain the graph of y = 3x + 2 Graph of the Equation XY(X,Y) -2-4(-2,-4) (-1,-1) 02(0,2) 15(1,5) 28(2,8)

7. Example Make a table of values for the equation y = 3x, and then use the table to graph this equation. Solution Start by selecting a few convenient values for x such as –1, 0, 1, and 2. Then complete the table. xy –1–3 00 13 26 Plot the points and connect the points with a straight line. Page 171

8. A linear equation in two variables can be written as Ax + By = C, where A, B, and C are fixed numbers (constants) and A and B are not both equal to 0. The graph of a linear equation in two variables is a line. Linear Equation in Two Variables Page 172

9. Example Graph the linear equation. Solution Because this equation can be written in standard form, it is a linear equation. Choose any three values for x. xy –40 01 42 Plot the points and connect the points with a straight line. Page 173

10. Example Graph the linear equation. Solution Because this equation can be written in standard form, it is a linear equation. Choose any three values for x. Plot the points and connect the points with a straight line. xy 05 23 50 Page 173

11. Example Graph the linear equation by solving for y first. Solution Solve for y. xy –21 02 23 Page 174

12. Plot the five ordered pairs to obtain the graph of y = 3x + 1 (2,7) (1,4) (0,1) (-1,-2) (-2,-5) Graph of the Equation XY(x,y) 27(2,7) 14(1,4) 01(0,1) -2(-1,-2) -2-5(-2,-5)

13. DONE

15. Tables of Solutions A table can be used to list solutions to an equation. A table that lists a few solutions is helpful when graphing an equation. Page 170

16. Basic Concepts Equations can have any number of variables. A solution to an equation with one variable is one number that makes the statement true. Page 168

17. Page 172

18. Example Graph the linear equation by solving for y first. Solution Solve for y. xy –21 02 23 Page 174

19. Plot the ordered pairs to obtain the graph of y = 2x Graph of the Equation

20. Plot the ordered pairs to obtain the graph of y = 2x-2 Graph of the Equation

21. Plot the ordered pairs to obtain the graph of Graph of the Equation

22. Plot the five ordered pairs to obtain the graph of y = 3x + 2 Graph of the Equation XY(x,y) -2-4(-2,-4) (-1,-1) 02(0,2) 15(1,5) 28(2,8)