1. Write Equations of Parallel and Perpendicular Lines

2. The converse of a conditional statement interchanges the hypothesis and conclusion
Parallel Lines
If two lines have the same slope, then they are parallel
If two lines are parallel, then they have the same slope

3. Example
Write an equation of the line that passes through (-3,-5) and is parallel to y=3x-1
Step 1 Find the slope. m= 3
Step 2 Write the equation using y=m(x-h)+k
y = 3(x-(-3))-5
y=3x+9-5
Y=3x+4

4. Example 2
Write an equation of the line that passes through (-2,11) and is parallel to y=-x+5
Step 1 Find the slope. m= -1
Step 2 Write the equation using y=m(x-h)+k
y = -1(x-(-2))+11
y=-x-2+11
Y=-x+9

5. Perpendicular Lines
Two lines are perpendicular if they intersect to form right angles. Horizontal and vertical lines are perpendicular to each other.
Perpendicular Lines
If two lines have slopes that are negative reciprocals, then they are perpendicular
If two lines are perpendicular, then their slopes are negative reciprocals

6. Example 3 Determine Whether the Lines are Parallel or Perpendicular
Line a: y=5x Line b: x+5y=2
Line c: -10y-2x=0
Line b: x+5y= Line c: -10y-2x=0
5y=-x y=2x y=
Lines b and c have slopes of so they are parallel. Line a has a slope of 5, so it is perpendicular to lines b and c.

7. Example 4 Determine Whether the Lines are Parallel or Perpendicular
Line a: 2x+6y=-3
Line b: y=3x-8
Line c: -1.5y+4.5x=6
Line a: 6y=-2x Line c: -1.5y=-4.5x+6
Lines b and c have the same slopes so they are parallel. The slope of line a is the negative reciprocal of the slope of line b and c, so it is perpendicular to lines b and c.

8. Example 5 Determine whether the lines are perpendicular
Line a: 3y=2x-1
Line b: 2y=-3x+21
Line a:
Line b:

9. Example 6 Determine whether the lines are perpendicular
line a: y=4x-2 line b:-4y-x=0
line b: -4y=x
Lines a and b are perpendicular

10. Example 7
Write an equation of the line that passes through (4,-5) and is perpendicular to the line y=2x+3.
Step 1: The slope must be
Step 2: Write the equation in y=m(x-h)+k form