1.1 Parallel and Perpendicular LinesPrecalculus

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Teacher Page Content: Write the equation of a parallel or

perpendicular line to a given line, in slope intercept form.

Parallel and Perpendicular Lines 3

Parallel Lines Two distinct 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 (2,-1) and is parallel to 2x – 3y = 5.

m = 2/3 and the point is (2,-1)

y = mx+b

-1 = 2/3(2)+b

-1 = 4/3+b

-7/3 = b

y = 2/3x-7/3

Now try independently Checkpoint Exercise 67 (a) pg 12

Extra Examples73, 68, 74, 76

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Write the equation of the line that passes through (2,1) and is parallel to 4x – 2y = 3.

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Perpendicular Lines Two non-vertical lines are

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

If m1= -1/m2 , then l1┴l2.

l1

l2

m2m1

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Write the equation of the line that passes through (2,-1) and is perpendicular to 2x- 3y =5.

m = 2/3 and the point is (2,-1)

y = mx+b

y = 2/3x – 5/3

-1 = -3/2(2)+b

-1 = -3+b

2 = b

y = -3/2x+2

Now Try Check point Exercise 67 (b) pg 12

Extra Examples73, 68, 74, 76

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Write the equation of the line that passes through (2,1) and is perpendicular to y = 4x – 2y =3.

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End Show

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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

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

m = _____ and the point is (__,__)

y = mx+b

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

m = ____ and the point is (__,__)

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

m=___ and the point is (__,__)

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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

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

m = ___ and the point is (__,-__)

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

m = ____ and the point is (__, __)

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

m = ___ and the point is (__,__)