3 3 Graphing Linear Equations in Two Variables

3. 3: Graphing Linear Equations in Two Variables Objectives: *Graph a linear equations in two variables. *Graph horizontal lines, vertical lines, and lines through the origin.

Linear Equation Definition Any equation that can be put in the form ax + by = c, where a, b, and c are real numbers and a and b are not both 0, is called a linear equation in two variables. The graph of any equation of this form is a straight line (that is why these equations are called “linear”). The form ax + by = c is called standard form.

Graphing Linear Equation Steps: Find any three ordered pairs that satisfy the equation. 2. Graph the 3 ordered pairs. 3. Draw a straight line through the 3 points. 1. *If the 3 points do not line up, there is a mistake. Go back and check the 3 ordered pairs.

Facts from Geometry Special Equations and Their Graphs For the equations below, m, a and b are real numbers. Through the Origin Vertical Line y = mx x=a Horizontal Line y=b

Problem Set 3. 3 (TB pp. 176 -177) Complete the given ordered pairs, and use the results to graph the solution set for the equation. 7. ) y = 1 x (-3, -1), (0, 0), (3, 1) 3 y = 1(-3) = -1 3 y = 1(0) = 0 3 y = 1(3) = 1 3 y=1 x 3

Problem Set 3. 3 (TB pp. 176 -177) Complete the given ordered pairs, and use the results to graph the solution set for the equation. 19. ) 3 x + 2 y = 6 (0, 3), (2, 0 ), (4, -3) 3 x + 2 y = 6 2 y = -3 x + 6 2 2 y = -3 x + 6 2 y = -3(0) + 6 = 3 2 y = -3(2) + 6 = 0 2 y = -3(4) + 6 = -3 2 3 x + 2 y = 6

Problem Set 3. 3 (TB pp. 176 -177) 41. Indicate whether the graph is horizontal (H), or vertical (V), or whether it passes through the origin (O). Equation H, V, & or O x=3 V y=3 H O O, H y = 3 x y=0 y = 3 x y=3 y=0 x=3

Problem Set 3. 3 (TB pp. 176 -177) Individual Practice: Homework Even Numbers Nos. 2, 4, 6… 46