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