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

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Presentation on theme: "4.3 Parallel and Perpendicular Lines Algebra 2/Geometry High School."— Presentation transcript:

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

2 MAP TAP Parallel and Perpendicular Lines 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 as a handout for students to take notes.

3 MAP TAP 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

4 MAP TAP Parallel and Perpendicular Lines 4 Parallel Lines Two non-vertical lines are parallel if and only if their slopes are equal. If l 1l 2, then m 1 = m 2. If m 1 = m 2, then l 1l 2. l1l1 l2l2 m1m1 m2m2

5 MAP TAP 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

6 MAP TAP 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

7 MAP TAP 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

8 MAP TAP Parallel and Perpendicular Lines 8 Perpendicular Lines Two non-vertical lines are perpendicular if and only if the product of their slopes is -1. If l 1l 2, then m 1 m 2 = -1. If m 1 m 2 = -1, then l 1l 2. l1l1 l2l2 m2m2 m1m1 Slopes are negative reciprocals

9 MAP TAP 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

10 MAP TAP 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

11 MAP TAP 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

12 MAP TAP Parallel and Perpendicular Lines 12 End Show

13 MAP TAP Parallel and Perpendicular Lines 13 Parallel Lines Two non-vertical lines are parallel if and only if their slopes are equal. If l 1l 2, then m 1 = m 2. If m 1 = m 2, then l 1l 2. l1l1 l2l2 m1m1 m2m2

14 MAP TAP 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

15 MAP TAP 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 (__,__)

16 MAP TAP 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 (__,__)

17 MAP TAP Parallel and Perpendicular Lines 17 Perpendicular Lines Two non-vertical lines are perpendicular if and only if the product of their slopes is -1. If l 1l 2, then m 1 m 2 = -1. If m 1 m 2 = -1, then l 1l 2. l1l1 l2l2 m2m2 m1m1

18 MAP TAP 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 (__,-__)

19 MAP TAP 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 (__, __)

20 MAP TAP 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 (__,__)


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