Parallel & Parallel & Perpendicular LinesPerpendicular Lines
Parallel & Parallel & Perpendicular LinesPerpendicular Lines
Parallel and Perpendicular LinesThe 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?• -2What is the slope of a line parallel to y = 4/7 x
– 1• 4/7What 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 1Line 2: rise = ___1___• Run 3The 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 + _____
41
-30
L1 L2
16
L1 L2
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
L1 L2
28
L1 L2
Top Related