1. Graphing Linear Equations in Two Variables Section 8.4

2. Linear Equation in Two Variables A linear equation in two variables variables is an equation that can be written in the form ax + by = c where, a,, b, and c are numbers, and a and b are not both.0..0. Examples 3x 3x 3x 3x + 2y 2y 2y 2y =6 y =8 3x 3x 3x 3x =4 Martin-Gay, Prealgebra, 5ed

3. Graphing Linear Equations by Plotting Points Every linear equation in two variables has infinitely many ordered-pair solutions. Since it is impossible to list every solution, we graph the solutions instead. The pattern described by the solutions of a linear equation makes “seeing” the solutions possible by graphing because all the solutions of a linear equation in two variables correspond to points on a single straight line. If we plot a few of these points and draw the straight line connecting them, we have a complete graph of all the solutions. Martin-Gay, Prealgebra, 5ed

4. To graph the equation, we plot a few ordered-pair solutions, say,, and. Then we connect the points. To graph the equation x + y = 5, we plot a few ordered-pair solutions, say (2,3), (0,5), and (-1, 6). Then we connect the points. 1 5 4 3 2 1 2345-1-2-2-3-3- 4- 4- 5- 5 x y (2,3) (0,5)(- 1,6) Martin-Gay, Prealgebra, 5ed

5. To Graph a Linear Equation in Two Variables  Find three ordered-pair solutions.  Graph the solutions.  Draw a line through the plotted points. Martin-Gay, Prealgebra, 5ed

6. To Find an Ordered-Pair Solution of an Equation  Choose either an x-value or y-value of the ordered pair.  Complete the ordered pair by replacing the variable with the chosen value and solving for the unknown variable. Martin-Gay, Prealgebra, 5ed

7. All three points should fall on the same straight line. If not, check your ordered-pair solutions for a mistake, since every linear equation is a line. Helpful Hint Martin-Gay, Prealgebra, 5ed

8. Horizontal Lines/Vertical Lines x y y = by = b x y x = ax = a Martin-Gay, Prealgebra, 5ed