Parallel Perpendicular Lines Parallel and Perpendicular Lines The

Parallel & Perpendicular Lines

Parallel and Perpendicular Lines The two lines shown below are parallel (never intersect). Identify the slope of each line. • Line 1: rise = • Run • Line 2: rise = • Run __2___ 3 • The slopes of parallel lines are__EQUAL__.

Parallel (Con’t) The slope of a line is -2. What is the slope of another line that is parallel to it? • -2 What is the slope of a line parallel to y = 4/7 x – 1 • 4/7 What is the slope of a line parallel to y = 3 + 5 x 5 Are the lines y = 2 x – 7 and y = 2 – 7 x parallel? NO

The two lines shown below are perpendicular (intersecting at right angles). Identify the slope of each line. Line 1: rise = __-3___ Run 1 Line 2: rise = ___1___ • Run 3 The slopes of perpendicular lines are _Opposite_ _Reciprocal__.

Perpendicular (Con’t) The slope of a line is ½. What is the slope of another line that is perpendicular to it? -2 What is the slope of a line perpendicular to y = -4 x + 1? 1/4 What is the slope of a line perpendicular to y = 8 + 5/2 x? -2/5 Are the lines y = 2 x – 7 and y = 1/2 x + 9 perpendicular? No

Equations of Parallel Lines • Write the equation of a line parallel to y = ¾ x – 2 with y-intercept = 5. y = __3/4___ x + __5___ • Write the equation of a line parallel to y = 4 x – 7 with y-intercept = -3. y = __4___ x + __-3___

Equations of Perpendicular Lines • Write the equation of a line perpendicular to y = 5 – 3 x with a y-intercept of 1. • Given slope = __-3___ Desired slope = __1/3___ • y = __1/3___ x + __1___ • Write the equation of a line perpendicular to y = 2/5 x – 3 with a y-intercept of 4. • Given slope = __2/5___ Desired slope = _-5/2____ • y = __-5/2___ x + __4___ • Write the equation of a line perpendicular to y = 9 + ¼ x with a y-intercept of -6. • Given slope = __1/4__ Desired slope = __-4___ • y = __-4___ x + __-6___

Equations of a Parallel Line through One Point • Write the equation of a line parallel to y = 7 x + 4 that passes through the point ( 1, 4 ). L L • 0 -3 y = __7___ x + _-3____ 1 2 1 4 • Write the equation of a line parallel to y = 8 – 2/3 x that passes through the point ( 6, 1 ). • y = _____ x + _____ L L 1 6 2 1

Write the equation of a line through the point ( -4, 5 ) that is perpendicular to y = 1/3 x – 4? Given slope = _____ Desired slope = _____ L L • y = _____ x + _____ 1 2 -4 5 Write the equation of a line through the point ( 8, 2 ) that is perpendicular to y = 7 – 4 x ? • Given slope = _____ Desired slope = _____ L L • y = _____ x + _____ 8 2 1 2