13.6 Graphing Linear Equations Geometry 13.6 Graphing Linear Equations

Graph on coordinate plane by using a t-chart Graph on coordinate plane by using a t-chart. Try to pick values of x that will give you integers. 1) 3x + 4y = 12 x y 3 .(0, 3) 4 . (4, 0) 8 -3 . (8, -3)

II. Standard Form: (Ax + By = C) II. Standard Form: (Ax + By = C). Getting x and y intercepts: (x, 0) and (0, y) 1) 2x + 3y = 6 2) 6x + 7y = 4 x y x y Try the cover up method!!! 4/7 2 Not too accurate… Plug in another point!!! 2/3 3 3 -2 .(0, 2) .(0, 4/7) . (3, 0) . (2/3, 0) .(3, -2)

II. Slope-Intercept Form (y = mx + b): m = slope; b = y-intercept y = 2x – 3 3. x = 3 4. y = 2 . . . 2. .(0, 4) . . . . . .(0, -3) . . .(3, 5) . . . .(3, 1) xertical yorizontal (-6, 2) (-1, 2) (6, 2) Why? Why? .(3, -4) .(3, -7) Thus y=2!! Thus x=3!!

III. Finding Slope-Intercept Form: (y = mx + b) 1. 2x + y = 6 m = _____ b = _____ 2) 3x – 4y = 10 3. x = y 4. x – 2y = 4y + 1 -2x -2x -3x -3x y = -2x + 6 -4y = -3x + 10 -4 -4 -4 y = 3/4x – 5/2 -2 6 -3/4 5/2 -4y -4y y = x x – 6y = 1 -x -x -6y = -x + 1 -6 -6 -6 y = 1/6x – 1/6 1 1/6 -1/6

.(2,4) IV. Systems of Equations: Two lines in a coordinate plane can do two things: (1) intersect (perpendicular or not) (2) not intersect (parallel) Systems Algebraic Graph By Substitution 2x + y = 8 y = 2x .(2,4) 2x + (2x) = 8 ( ) ( ) 4x = 8 x = 2 y = -2x + 8 Substitute 2 back in for x in the easier equation!! Isolate a variable first. This is already done. Then substitute. y = 2x y = 2x Graph 2x + y = 8 y = 2(2) -2x -2x y = 4 y = -2x + 8 The solution to the system is (2, 4) Graph y = 2x

. IV. Systems of Equations: Two lines in a coordinate plane can do two things: (1) intersect (perpendicular or not) (2) not intersect (parallel) Systems Algebraic Graph By Addition x – 6y = -3 3x + 6y = 15 3(3) + 6y = 15 y = -1/2x + 5/2 . (3,1) 9 + 6y = 15 y = 1/6x + 1/2 -9 -9 4x = 12 6y = 6 x = 3 y = 1 Substitute 3 back in for x in the easier equation!! Graph x – 6y = -3 The solution to the system is (3, 1) -x -x -6y = -x – 3 Graph 3x + 6y = 15 -6 -6 -6 -3x -3x y = 1/6x + 1/2 6y = -3x + 15 6 6 6 y = -1/2x + 5/2

. IV. Systems of Equations: Two lines in a coordinate plane can do two things: (1) intersect (perpendicular or not) (2) not intersect (parallel) Systems Algebraic Graph By Addition w/Multiplication 2x + y = 6 3x – 2y = 2 4(2) + 2y = 12 . (2,2) 4x + 2y = 12 ( )2 8 + 2y = 12 -8 -8 2y = 4 7x = 14 y = 3/2x – 1 y = 2 y = -2x + 6 x = 2 Substitute 2 back in for x in the easier equation!! Graph 2x + y = 6 The solution to the system is (2, 2) -2x -2x y = -2x + 6 Graph 3x – 2y = 2 -3x -3x -2y = -3x + 2 -2 -2 -2 y = 3/2x – 1

1. 2x + y = 8 3x – y = 2 2. x – 6y = –3 3x + 6y = 15 3. 2x + y = 6 Solve the following systems of equations. 1. 2x + y = 8 3x – y = 2 2. x – 6y = –3 3x + 6y = 15 3. 2x + y = 6 3x – 2y = 2 4. 2x + y = –2 2x – 3y = 14 (2,4) (3,1) (2,2) (1,-4) Note: After you solve, you can always plug in your solution to check.

HW Next time you debate on doing something good, do it!