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2.2 Linear Equations

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SLOPE RISE RUN SLOPE

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Slope Formula Given points (X 1,Y 1 ) and (X 2,Y 2 ) Is the same as ?

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Example ( 4, 0 ) and ( 7, 6 ) (X 1,Y 1 ) (X 2,Y 2 )

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Example ( -6, 5 ) and ( 2, 4 ) (X 1,Y 1 ) (X 2,Y 2 )

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Example ( 5, 2 ) and ( -3, 2 ) (X 1,Y 1 ) (X 2,Y 2 )

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Example ( 2, 7 ) and ( 2, -3 ) (X 1,Y 1 ) (X 2,Y 2 )

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Recap of slope

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Linear Forms of Linear Equations Standard Form (AX + BY = C) 1)A and B cannot be fractions. 2)A cannot be negative y = 3x – 5 y – 3x = – 5 – 3x + y = – 5 3x – y = 5 To find y-intercept, set x = 0 Y-intercept (0,-5) FINDING INTERCEPTS To find x-intercept, set y = 0 X-intercept (5/3,0)

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Linear Forms of Linear Equations Slope Intercept Form (y = mx + b) 1)Y is isolated on one side. 2)Y is positive x – 2y = 6 –2y = – x + 6 y = ½ x + 6/-2 y = ½ x – 3 To find y-intercept, set x = 0 Y-intercept (0,-3) FINDING INTERCEPTS To find x-intercept, set y = 0 X-intercept (6,0)

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Find a line || to 2x + 4y = -8 and passes thru (8,3) First find slope 2x + 4y = -8 4y = -2x – 8 y = - ½ x – 2 Slope Use y = mx + b y = - 1/2x + b Plug in point 3 = - ½ (8) + b 3 = -4 + b 7 = b FINAL EQUATION y = mx + b y = - ½ x + 7 Slope intercept

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Find a line Perpendicular to 3x – 2y = 10 and passes thru (-6,2) First find slope 3x – 2y = y = -3x + 10 y = 3/2 x – 5 Slope Use y = mx + b y = -2/3 x + b Plug in point 2 = -2/3 (-6) + b 2 = 4+ b -2 = b FINAL EQUATION y = mx + b y = -2/3x - 2 Slope intercept c

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Find a line That has slope = 2 and passes thru (-4,7) Use y = mx + b y = 2x + b Plug in point 7 = 2 (-4) + b 7 = -8 + b 15 = b FINAL EQUATION y = mx + b y = 2 x + 15 Slope intercept

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Find a line That has x-intercept = (5,0) and y-intercept (0,-3) Use y = mx + b y = 3/5 x + b Plug in point either one ! 0 = 3/5 (5) + b 0 = 3 + b -3 = b FINAL EQUATION y = mx + b y = 3/5 x - 3 Slope intercept First find slope m m = 3/5

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First Let’s Review... Graphing Linear Equations

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Graph x = 3

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Graph y = -3

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Graph Y = -3/4 x + 2 Y = mx + b m = slope b = y-intercept 1)Plot the y-intercept first 2)Starting from the y-intercept, go up if + or down if – Then go right. 3) Plot point and draw your line. m = -3 / 4 b = 2

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Graph 5x + 6y < 30 5x + 6y < 30 6y< -5x + 30 Y < -5/6 x +5

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Graph 2x + 4y ≥ 16 2x + 4y ≥ 16 4y ≥ -2x + 16 Y ≥ -2/4 x + 4 Y ≥ -1/2 x + 4

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Graph 5x - y < 8 5x – y < 8 – y < -5x + 8 y > 5x – 8

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