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GRAPHING LINEAR EQUATIONS PARALLEL VS PERPENDICULAR LINES WARM-UP: Find the slope and y-intercept of the following linear equations 1. Y + 3 = 2x 2. Y + 3x = -6 Y = 2x - 3 Slope: 2 Y-int: -3 Y = -3x - 6 Slope: -3 Y-int: -6 3. y - x - 21= 3 Y = x + 24 Slope: 1 Y-int: 24 4. 3Y + 9 = 6x 5. 2y + 3 = 2x 6. 4y - x - 2= 3 Y = 2x - 3 Y = x - 3/2 Y = x/4 +5/4 Slope: 2 Slope: 1 Slope: 1/4 Y-int: -3 Y-int: -3/2 Y-int: 5/4 Parallel lines Parallel lines are linear equations which have the same slope Examples: Y=2x+9 Y=2x-23 Y=1/3x +10 Y=1/3x +5 Y=x +10 Y=7 +x Counter-examples: Y=-2x+9 Y=2x-23 Y=1/3x +10 Y=3x +5 Y=5x +10 Y=7 +x Example: 2x + 6y = 12 -2x -2x 6y = -2x + 12 6 6 6 y = -2/6 x + 2 y = -1/3 x + 2 Is parallel to y = -1/3 x + 5 REVIEW Find the reciprocal of the following numbers: 1. ⅔ 3/2 2. ⅜ 3. 8/3 7 4. 1/7 1/9 9 Find the negative reciprocal of the following numbers: 1. ½ -2 2. 4/9 -9/4 3. 8/7 -7/8 4. 3 -⅓ Perpendicular lines THE LINES ARE PERPENDICULAR IF THE PRODUCT OF THEIR SLOPES Examples: IS -1. Y=2x+9 Y=-½x-23 Y=1/3x +10 Y=-3x +5 Y=x +10 Y=-1X +21 Counter-examples: Y=-2x+9 Y=-2x-23 Y=⅓x +10 Y=3x +10 Y=5x +10 Y=7 +x Example: Write an equation that is perpendicular to the following: 1. Y = 2/3x + 7 Y = -3/2x + 7 3. Y = -1/9x + 29 Y = 9x + 879 2. Y = 7x -9 Y = -1/7x + 25 4. Y = -5x - 6 Y = -⅕x + 25 Practice re the equations parallel to each other? no no yes yes yes yes Which one is a parallel line? Which one is a perpendicular line? perpendicular perpendicular parallel niether