§ 1.2 Graphing Linear Equations

Martin-Gay, Beginning and Intermediate Algebra, 4ed 22 Linear Equation in Two Variables A linear equation in two variables is an equation that can be written in the form Ax + By = C where A, B, and C are real numbers and A and B are not both 0. The graph of a linear equation in two variables is a straight line. The form Ax + By = C is called standard form. Linear Equations

Martin-Gay, Beginning and Intermediate Algebra, 4ed 33 Graph the linear equation 2x – y = – 4. We find two ordered pair solutions (and a third solution as a check on our computations) by choosing a value for one of the variables, x or y, then solving for the other variable. We plot the solution points, then draw the line containing the 3 points. Example: Graphing Linear Equations Continued.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 44 Graph the linear equation 2x – y = – 4. Let x = 1. 2(1) – y = – 4 Replace x with 1. 2 – y = – 4 Simplify the left side. – y = – 4 – 2 = – 6 Subtract 2 from both sides. y = 6 Multiply both sides by – 1. One solution to the equation is (1, 6). Example continued: Graphing Linear Equations Continued.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 55 Graph the linear equation 2x – y = – 4. For the second solution, let y = 4. 2x – 4 = – 4 Replace y with 4. 2x = – Add 4 to both sides. 2x = 0 Simplify the right side. x = 0 Divide both sides by 2. The second solution is (0, 4). Graphing Linear Equations Example continued: Continued.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 66 Graph the linear equation 2x – y = – 4. For the third solution, let x = – 3. 2(– 3) – y = – 4 Replace x with – 3. – 6 – y = – 4 Simplify the left side. – y = – = 2 Add 6 to both sides. y = – 2 Multiply both sides by – 1. The third solution is (– 3, – 2). Graphing Linear Equations Example continued: Continued.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 77 Now plot all three of the solutions (1, 6), (0, 4) and (– 3, – 2). x y (1, 6) (0, 4) (– 3, – 2) Draw the line that contains the three points. Graphing Linear Equations Example continued:

Martin-Gay, Beginning and Intermediate Algebra, 4ed 88 Let x = 4. y = = 6 S implify the right side. One solution is (4, 6). Graph the linear equation y = x + 3. y = (4) + 3 R eplace x with 4. Graphing Linear Equations Example: Continued.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 99 For the second solution, let x = 0. y = = 3 S implify the right side. So a second solution is (0, 3). Graph the linear equation y = x + 3. y = (0) + 3 R eplace x with 0. Graphing Linear Equations Example continued: Continued.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 10 For the third solution, let x = – 4. y = – = 0 S implify the right side. The third solution is ( – 4, 0). Graph the linear equation y = x + 3. y = ( – 4) + 3 Replace x with – 4. Example continued: Graphing Linear Equations Continued.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 11 Plot all three of the solutions (4, 6), (0, 3) and (– 4, 0). x y (4, 6) (0, 3) (– 4, 0) Draw the line that contains the three points. Graphing Linear Equations Example continued: