Section 3.1 Parallel and Perpendicular Lines

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Parallel Lines – lie on same plane and never intersect

Perpendicular Lines – intersects to form a right angle

Skew Lines – do not lie on the same plane, never intersects

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Parallel Lines (Algebra Review)

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

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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

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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

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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

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Perpendicular Lines (Algebra Review)

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

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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

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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

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

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

y = -x-7

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What’s going on in this graph?

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skew lines can exist only in three or more dimensions.

Skew Lines

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Which lines are skew?

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What’s going on here?

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Which lines are parallel?

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Main Idea

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Over head examples

In-Class practice problems

Homeworkp110-111 #1-19 & 25-29