# 4.3 Parallel and Perpendicular Lines

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4.3 Parallel and Perpendicular Lines

4.3 Parallel and Perpendicular Lines Algebra 2/Geometry High School 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. MAP TAP 2003-2004 Parallel and Perpendicular Lines 2 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 MAP TAP 2003-2004 Parallel and Perpendicular Lines 3 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. m1 l1 MAP TAP 2003-2004 Parallel and Perpendicular Lines m2 l2 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 MAP TAP 2003-2004 Parallel 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 MAP TAP 2003-2004 Parallel 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 MAP TAP 2003-2004 Parallel and Perpendicular Lines 7 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. l1 If m1● m2 = -1, then l1┴l2. Slopes are negative reciprocals MAP TAP 2003-2004 Parallel and Perpendicular Lines m1 m2 l2 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 MAP TAP 2003-2004 Parallel 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 MAP TAP 2003-2004 Parallel 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 MAP TAP 2003-2004 Parallel and Perpendicular Lines 11 End Show MAP TAP 2003-2004 Parallel and Perpendicular Lines 12 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. m1 l1 MAP TAP 2003-2004 Parallel and Perpendicular Lines m2 l2 13 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 MAP TAP 2003-2004 Parallel and Perpendicular Lines 14 Write the equation of the line that passes through (4,-5) and is parallel to y = -2x-4. m = ____ and the point is (__,__) MAP TAP 2003-2004 Parallel and Perpendicular Lines 15 Write the equation of the line that passes through (-6,4) and is parallel to y=1/3x-1. m=___ and the point is (__,__) MAP TAP 2003-2004 Parallel and Perpendicular Lines 16 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. l1 If m1● m2 = -1, then l1┴l2. m1 m2 l2 MAP TAP 2003-2004 Parallel and Perpendicular Lines 17 Write the equation of the line that passes through (6,-5) and is perpendicular to y = 2x+3. m = ___ and the point is (__,-__) MAP TAP 2003-2004 Parallel and Perpendicular Lines 18 Write the equation of the line that passes through (6,-7) and is perpendicular to y = 2/3x+1. m = ____ and the point is (__, __) MAP TAP 2003-2004 Parallel and Perpendicular Lines 19 Write the equation of the line that passes through (-4,-3) and is perpendicular to y = x+6. m = ___ and the point is (__,__) MAP TAP 2003-2004 Parallel and Perpendicular Lines 20