GRAPHING LINEAR EQUATIONS PARALLEL VS PERPENDICULAR LINES

WARM-UP: Find the slope and y-intercept of the following linear equations 1. Y + 3 = 2 x 2. Y + 3 x = -6 Y = 2 x - 3 Slope: 2 Y-int: -3 Y = -3 x - 6 Slope: -3 Y-int: -6 3. y - x - 21= 3 Y = x + 24 Slope: 1 Y-int: 24 4. 3 Y + 9 = 6 x 5. 2 y + 3 = 2 x 6. 4 y - x - 2= 3 Y = 2 x - 3 Y = x - 3/2 Y = x/4 +5/4 Slope: 2 Slope: 1/4 Y-int: -3/2 Y-int: 5/4

Parallel lines are linear equations which have the same slope Examples: Y=2 x+9 Y=2 x-23 Y=1/3 x +10 Y=1/3 x +5 Y=x +10 Y=7 +x Counter-examples: Y=-2 x+9 Y=2 x-23 Y=1/3 x +10 Y=3 x +5 Y=5 x +10 Y=7 +x

Example: 2 x + 6 y = 12 -2 x 6 y = -2 x + 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=2 x+9 Y=-½x-23 Y=1/3 x +10 Y=-3 x +5 Y=x +10 Y=-1 X +21 Counter-examples: Y=-2 x+9 Y=-2 x-23 Y=⅓x +10 Y=3 x +10 Y=5 x +10 Y=7 +x

Example: Write an equation that is perpendicular to the following: 1. Y = 2/3 x + 7 Y = -3/2 x + 7 3. Y = -1/9 x + 29 Y = 9 x + 879 2. Y = 7 x -9 Y = -1/7 x + 25 4. Y = -5 x - 6 Y = -⅕x + 25

Practice re the equations parallel to each other? no no yes yes Which one is a parallel line? Which one is a perpendicular line? perpendicular parallel niether