4.3 Parallel and Perpendicular Lines

1. 4.3 Parallel and Perpendicular Lines Algebra 2/Geometry High School

2. Teacher Page • Content: Write the equation of a parallel or perpendicular line to a given line, in slope intercept form. • Grade Level: Algebra 2/Geometry • Creator: Don Sutcliffe • Other – Print slides 13-20 as a handout for students to take notes. Parallel and Perpendicular Lines

3. Teacher Page • Curriculum Objectives: • Algebra 2 – II.A – The learner will find the slope of a linear equation and the relationships of the slopes of parallel and perpendicular lines. • MAP Objectives: • Missouri Show-Me Standard – Math – MA1, MA2, MA4, MA5 • Missouri Show-Me Standard – Goal – G1.6, G3.4, G3.5, G4.1 Parallel and Perpendicular Lines

4. 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. Parallel Lines m1 m2 l1 l2 Parallel and Perpendicular Lines

5. 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

6. 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

7. 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

8. 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. Perpendicular Lines m1 l1 m2 Slopes are negative reciprocals l2 Parallel and Perpendicular Lines

9. 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

10. 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 Parallel and Perpendicular Lines

11. 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 Parallel and Perpendicular Lines

12. End Show Parallel and Perpendicular Lines

13. 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. Parallel Lines m1 m2 l1 l2 Parallel and Perpendicular Lines

14. 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 Parallel and Perpendicular Lines

15. Write the equation of the line that passes through (4,-5) and is parallel to y = -2x-4. m = ____ and the point is (__,__) Parallel and Perpendicular Lines

16. Write the equation of the line that passes through (-6,4) and is parallel to y=1/3x-1. m=___ and the point is (__,__) Parallel and Perpendicular Lines

17. 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. Perpendicular Lines m1 l1 m2 l2 Parallel and Perpendicular Lines

18. Write the equation of the line that passes through (6,-5) and is perpendicular to y = 2x+3. m = ___ and the point is (__,-__) Parallel and Perpendicular Lines

19. Write the equation of the line that passes through (6,-7) and is perpendicular to y = 2/3x+1. m = ____ and the point is (__, __) Parallel and Perpendicular Lines

20. Write the equation of the line that passes through (-4,-3) and is perpendicular to y = x+6. m = ___ and the point is (__,__) Parallel and Perpendicular Lines