4.4 Parallel and Perpendicular LinesAlgebra

Mr. Knighton

Parallel and Perpendicular Lines 2

Parallel Lines Two non-vertical lines are parallel if

and only if their slopes are equal. If l1║l2, then m1= m2.

If m1= m2, then l1║l2.

l1 l2

m1 m2

Parallel and Perpendicular Lines 3

Write the equation of the line that passes through (3,6) and is parallel to y = 2/3x+2.

m = 2/3 and the point is (3,6)

y = mx+b

6 = 2/3(3)+b

6 = 2+b

4 = b

y = 2/3x+4

Parallel and Perpendicular Lines 4

Write the equation of the line that passes through (4,-5) and is parallel to y = -2x-4.

m = -2 and the point is (4,-5)

y = mx+b

-5 = -2(4)+b

-5 = -8+b

3 = b

y = -2x+3

Parallel and Perpendicular Lines 5

Write the equation of the line that passes through (-6,4) and is parallel to y=1/3x-1.

m=1/3 and the point is (-6,4)

y =1/3x+6

Parallel and Perpendicular Lines 6

Perpendicular Lines Two non-vertical lines are

perpendicular if and only if the product of their slopes is -1. If l1┴l2, then m1 ● m2= -1.

If m1● m2 = -1, then l1┴l2.l1

l2

m2m1

Slopes are negative reciprocals

Parallel and Perpendicular Lines 7

Write the equation of the line that passes through (6,-5) and is perpendicular to y = 2x+3.

m = -1/2 and the point is (6,-5)

y = mx+b

-5 = -1/2(6)+b

-5 = -3+b

-2 = b

y = -1/2x-2

Parallel and Perpendicular Lines 8

Write the equation of the line that passes through (6,-7) and is perpendicular to y = 2/3x+1.

m = -3/2 and the point is (6,-7)

y = mx+b

-7 = -3/2(6)+b

-7 = -9+b

2 = b

y = -3/2x+2