3-2 Graphs of Linear Equations in 2 Variables

Coordinate Plane y-axis (x,y) Right (+) Up (+) Left (-) Down (-) origin x-axis

Standard Form Ax + By = C A,B,C are all integers Any linear equation can be written in this form Linear equation: Makes a line when graphed Examples NOT Examples x + 3y = 9 2x + 3y2 = 6 y = 5 xy = 2 y = 3x – 5

Graphing Standard Form Find the x- and y-intercepts x-intercept = crosses the x-axis (x,0) y-intercept = crosses the y-axis (0,y) Example x – 2y = 6 x-intercept: x – 2(0) = 6 (6,0) y-intercept: 0 – 2y = 6 (0,-3) COVER UP METHOD Cover up the letter you are not looking for an divide Must be in STANDARD FORM to use cover-up

Graph Continued (6,0)(0,-3)

TOO Graph using intercepts 1) x – y = 3 2) 3x + 2y – 9 = 0 Intercepts: 1) (3,0)(0,-3) 2) (3,0)(0,4.5)

Example 2x – 3y = 0 (0,0) (3,2) You need one more point Pick an x and solve for y 2(3) – 3y = 0 y = 2

TOO Graph 1) 2x + 5y = 0 2) x = y Possible Points: 1) (0,0)(5,-2) 2) (0,0)(1,1)

Example: One Variable x = 3 Vertical Line y = -2 Horizontal Line TOO: 2x + 1 = 0 x = -0.5

Homework