PARALLEL AND PERPENDICULAR

LINESALGEBRA 2/GEOMETRY

HIGH SCHOOL

PARALLEL LINES

MAP TAP 2003-2004

Parallel and Perpendicular Lines 2

• 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

WRITE THE EQUATION OF THE LINE THAT PASSES THROUGH (3,6) AND IS PARALLEL TO Y = 2 X+2

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

y = mx+b6 = 2/3(3)+b6 = 2+b4 = b

y = 2/3x+4 MAP TAP 2003-2004

Parallel and Perpendicular Lines

3

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+b3 = b

y = -2x+3MAP TAP 2003-2004

Parallel and Perpendicular Lines 4

WRITE THE EQUATION OF THE LINE THAT PASSES THROUGH (-6,4) AND IS

PARALLEL TO Y= 1 X-1

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

y =1/3x+6MAP TAP 2003-2004

Parallel and Perpendicular Lines 5

PERPENDICULAR LINES

Parallel and Perpendicular Lines 6

• 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

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 x-2 2

MAP TAP 2003-2004

Parallel and Perpendicular Lines 7

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+b2 = b

y = -3 x+2 2

MAP TAP 2003-2004

Parallel and Perpendicular Lines 8

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-7MAP TAP 2003-2004

Parallel and Perpendicular Lines 9