Parallel & Perpendicular Lines. Parallel and Perpendicular Lines The two lines shown below are parallel (never intersect). Identify the slope of each.

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Presentation transcript:

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 =__2___ Run 3 Line 2:rise =__2___ Run 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 = 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 ). y = __7___ x + _-3____ Write the equation of a line parallel to y = 8 – 2/3 x that passes through the point ( 6, 1 ). y = _____ x + _____ L 1 L 2 16

Write the equation of a line through the point ( -4, 5 ) that is perpendicular to y = 1/3 x – 4 ? Given slope = _____ Desired slope = _____ y = _____ x + _____ Write the equation of a line through the point ( 8, 2 ) that is perpendicular to y = 7 – 4 x ? Given slope = _____ Desired slope = _____ y = _____ x + _____ 5-4 L 1 L 2 28

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