4.4 Parallel and Perpendicular Lines

1
4.4 Parallel and Perpendicular Lines

• Algebra
• Mr. Knighton

2
Parallel Lines

• Two non-vertical lines are parallel if and only
  if their slopes are equal.
• If l1l2, then m1 m2.
• If m1 m2, then l1l2.

m1
m2
l1
l2
3
Write the equation of the line that passes
through (3,6) and is parallel to y 2/3x2.

• m 2/3 and the point is (3,6)
• y mxb
• 6 2/3(3)b
• 6 2b
• 4 b
• y 2/3x4

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 mxb
• -5 -2(4)b
• -5 -8b
• 3 b
• y -2x3

5
Write the equation of the line that passes
through (-6,4) and is parallel to y1/3x-1.

• m1/3 and the point is (-6,4)
• y 1/3x6

6
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.
• If m1? m2 -1, then l1-l2.

m1
l1
m2
Slopes are negative reciprocals
l2
7
Write the equation of the line that passes
through (6,-5) and is perpendicular to y 2x3.

• m -1/2 and the point is (6,-5)
• y mxb
• -5 -1/2(6)b
• -5 -3b
• -2 b
• y -1/2x-2

8
Write the equation of the line that passes
through (6,-7) and is perpendicular to y 2/3x1.

• m -3/2 and the point is (6,-7)
• y mxb
• -7 -3/2(6)b
• -7 -9b
• 2 b
• y -3/2x2