3-2 Graphs of Linear Equations in 2 Variables

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3-2 Graphs of Linear Equations in 2 Variables
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Coordinate Plane
y-axis
(x,y)
Up () Down (-)
Right () Left (-)
origin
x-axis
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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

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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
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Graph Continued

• (6,0)(0,-3)

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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)

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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

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TOO

• Graph
• 1) 2x 5y 0 2) x y
• Possible Points
• 1) (0,0)(5,-2) 2) (0,0)(1,1)

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Example One Variable

• x 3
• Vertical Line
• y -2
• Horizontal Line
• TOO 2x 1 0
• x -0.5

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Homework