1. Section 3.1 Parallel and Perpendicular Lines

2. MAP TAP 2003-2004Parallel and Perpendicular Lines 2 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

3. MAP TAP 2003-2004Parallel and Perpendicular Lines 3 Parallel Lines (Algebra Review)  Two non-vertical lines are parallel if and only if their slopes are equal. If l 1 ║l 2, then m 1 = m 2. If m 1 = m 2, then l 1 ║l 2. l1l1 l2l2 m1m1 m2m2

4. MAP TAP 2003-2004Parallel and Perpendicular Lines 4 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

5. MAP TAP 2003-2004Parallel and Perpendicular Lines 5 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

6. MAP TAP 2003-2004Parallel and Perpendicular Lines 6 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

7. MAP TAP 2003-2004Parallel and Perpendicular Lines 7 Perpendicular Lines (Algebra Review)  Two non-vertical lines are perpendicular if and only if the product of their slopes is -1. If l 1 ┴l 2, then m 1 ● m 2 = -1. If m 1 ● m 2 = -1, then l 1 ┴l 2. l1l1 l2l2 m2m2 m1m1 Slopes are negative reciprocals

8. MAP TAP 2003-2004Parallel and Perpendicular Lines 8 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

9. MAP TAP 2003-2004Parallel and Perpendicular Lines 9 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

10. MAP TAP 2003-2004Parallel and Perpendicular Lines 10 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

11. MAP TAP 2003-2004Parallel and Perpendicular Lines 11 What’s going on in this graph?

12. MAP TAP 2003-2004Parallel and Perpendicular Lines 12

13. MAP TAP 2003-2004Parallel and Perpendicular Lines 13 skew lines can exist only in three or more dimensions. dimensions Skew Lines

14. MAP TAP 2003-2004Parallel and Perpendicular Lines 14 Which lines are skew?

15. MAP TAP 2003-2004Parallel and Perpendicular Lines 15 What’s going on here?

16. MAP TAP 2003-2004Parallel and Perpendicular Lines 16 Which lines are parallel?

17. MAP TAP 2003-2004Parallel and Perpendicular Lines 17 Main Idea

18. MAP TAP 2003-2004Parallel and Perpendicular Lines 18

19. MAP TAP 2003-2004Parallel and Perpendicular Lines 19 Over head examples In-Class practice problems Homework p110-111 #1-19 & 25-29