Chapter 3.3 Slopes of Lines

Chapter 3.3 Slopes of Lines Objective: Be able to calculate slope of line and determine if lines are parallel, perpendicular or neither 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).

Slope m = rise = change in y. = y2 – y1 run change in x x2 – x1 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? m= 0 4 –4 -3 –4 -7 m= m= m= 2 3-3 0 m = undefined

Slope of Parallel and Perpendicular Lines y = 3/4x + 2 m = 3/4 y = 3/4x - 5 is ________ Parallel Perpendicular y = -4/3x + 3 is ____________

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) -4 -2 –2 12 7–(-5) CD= AB= AB= CD= 8 –0 6 8 4 –(-2) Perpendicular AB=2 CD= - 1/2

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) 12 7-(-5) 3 -4–(-7) CD= AB= AB= CD= 1-(-2) 12 3 4 –(-8) Neither AB=1/4 CD= 4

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) Perpendicular Slope = -5/2 -2–(-4) 2 JK= JK= 0 –(-5) 5 y = -5/2x - 4

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

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

Practice Assignment • Block - Page 190, 12 - 36 every 4th

Chapter 3.3 Slopes of Lines