Chapter 3.3 Slopes of Lines Check.3.1 Prove two lines are parallel, perpendicular, or oblique using coordinate geometry. Spi.3.1 Use algebra and coordinate.

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Presentation transcript:

Chapter 3.3 Slopes of Lines Check.3.1 Prove two lines are parallel, perpendicular, or oblique using coordinate geometry. Spi.3.1 Use algebra and coordinate geometry to analyze and solve problems about geometric figures (including circles). Objective: Be able to calculate slope of line and determine if lines are parallel, perpendicular or neither

Slopem = rise = change in y. = y 2 – y 1 run change in x x 2 – x 1 Horizontal Line, m= 0 Vertical Line, m = undefined Lines are parallel if m = m Lines are perpendicular if m = -1/m

What is the slope? 4 –4 m= 2 m= 0 -3 –4 m= m= 0 m = undefined

Slope of Parallel and Perpendicular Lines Two non-vertical lines have the same slope if and only if they are parallel Two non-vertical lines are perpendicular if and only if the product of their slopes is -1 y = 3/4x + 2 m = y = 3/4x - 5 is ________ y = -4/3x + 3 is ____________ Parallel Perpendicular 3/4

Parallel and Perpendicular Lines y = 2x + 2 Parallel Line through (0,0) y = 2x Perpendicular through (0,0) y = - ½ x

Determine line relationships Determine whether AB and CD are parallel, perpendicular or neither A (-2, -5) B(4, 7) C(0, 2) D(8, -2) 7–(-5) AB= 4 –(-2) -2 –2 CD= 8 –0 12 AB= 6 -4 CD= 8 AB=2 CD= - 1/2 Perpendicular

Determine line relationships Determine whether AB and CD are parallel, perpendicular or neither A (-8, -7) B(4, -4) C(-2, -5) D(1, 7) -4–(-7) AB= 4 –(-8) 7-(-5) CD= 1-(-2) 3 AB= 12 CD= 3 AB=1/4 CD= 4 Neither

Use Slope to find a line Draw a line containing P (-2,1) and is perpendicular to JK with J(-5, -4) and K(0,-2) -2–(-4) JK= 0 –(-5) 2 JK= 5 Perpendicular Slope =-5/2 y = -5/2x - 4

Write equation from 2 points A (-1, 6) and B (3, 2) 2 –6 m= 3 –(-1) -4 m= 4 m= -1 6 = -1(-1) + b y = mx + b 6 = 1 + b 5= b y = -x + 5

Write equation from 2 points A (4, 9) and B (-2, 0) 0 –9 m= -2 –4 -9 m= -6 m= 3/2 9 = 3/2(4) + b y = mx + b 9 = 6 + b 3= b y = 3/2x + 3

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