1. 4.4 Parallel and Perpendicular Lines Algebra Mr. Knighton

2. Parallel and Perpendicular Lines 2 Parallel Lines  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

3. Parallel and Perpendicular Lines 3 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

4. Parallel and Perpendicular Lines 4 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

5. Parallel and Perpendicular Lines 5 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

6. Parallel and Perpendicular Lines 6 Perpendicular Lines  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

7. Parallel and Perpendicular Lines 7 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

8. Parallel and Perpendicular Lines 8 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