1. Parallel & Perpendicular Lines
Comparing the slope of 2 lines determines if those lines are parallel, perpendicular, or just intersecting ( neither ).
Parallel Lines – slopes are EQUAL
Perpendicular lines – slopes are reciprocal AND opposite signs

2. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
( 6 , 4 )
( 2 , - 2 )

3. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
Use the slope formula :
( 6 , 4 )
( x1 , y1 )
( 2 , - 2 )
( x2 , y2 )

4. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
Use the slope formula :
( 6 , 4 )
( x1 , y1 )
( 2 , - 2 )
( x2 , y2 )

5. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
Use the slope formula :
Answer
( 6 , 4 )
( x1 , y1 )
Parallel lines have the SAME slope…
( 2 , - 2 )
( x2 , y2 )

6. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
You could have also just counted the slope from the graph…start at one point and count…
+ 4
( 6 , 4 )
+ 6
( 2 , - 2 )

7. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to the line on the graph.
You could have also just counted the slope from the graph…start at one point and count…
+ 4
( 6 , 4 )
+ 6
( 2 , - 2 )
Answer

8. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to

9. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to
Let’s solve for y and get the equation into y = mx + b form…

10. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to
Let’s solve for y and get the equation into y = mx + b form…

11. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to
Let’s solve for y and get the equation into y = mx + b form…

12. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to
Let’s solve for y and get the equation into y = mx + b form…
Here’s the slope…

13. Parallel & Perpendicular Lines
Parallel Lines – slopes are EQUAL
EXAMPLE : Find the slope of all lines parallel to
Let’s solve for y and get the equation into y = mx + b form…
So parallel slope would be the SAME …
Answer
Here’s the slope…

14. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the line on the graph.
Use the slope formula :
( x1 , y1 )
( - 6 , - 2 )
( x2 , y2 )
( - 1 , - 5 )

15. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the line on the graph.
Use the slope formula :
( x1 , y1 )
( - 6 , - 2 )
( x2 , y2 )
( - 1 , - 5 )

16. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the line on the graph.
Use the slope formula :
( x1 , y1 )
To get the perpendicular slope, flip the fraction and change the sign…
( - 6 , - 2 )
( x2 , y2 )
( - 1 , - 5 )

17. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the line on the graph.
Use the slope formula :
( x1 , y1 )
To get the perpendicular slope, flip the fraction and change the sign…
( - 6 , - 2 )
( x2 , y2 )
( - 1 , - 5 )
Answer

18. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the given equation.

19. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the given equation.
Solve for “y” and get equation into y = mx + b form

20. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the given equation.

21. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
EXAMPLE : Find the slope of all lines perpendicular to the given equation.
To get the perpendicular slope, flip the fraction and change the sign…
Answer

22. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
Parallel Lines – slopes are EQUAL
EXAMPLE : Are the given equations parallel, perpendicular, or neither.

23. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
Parallel Lines – slopes are EQUAL
EXAMPLE : Are the given equations parallel, perpendicular, or neither.
Compare the slopes :
- not the same ( different signs )
- not reciprocal
Therefore they are NEITHER

24. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
Parallel Lines – slopes are EQUAL
EXAMPLE : Are the given equations parallel, perpendicular, or neither.

25. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
Parallel Lines – slopes are EQUAL
EXAMPLE : Are the given equations parallel, perpendicular, or neither.
Get both equations into y = mx + b form

26. Parallel & Perpendicular Lines
Perpendicular lines – slopes are reciprocal AND opposite signs
Parallel Lines – slopes are EQUAL
EXAMPLE : Are the given equations parallel, perpendicular, or neither.
Perpendicular
Compare slopes…
- not the same
- they are reciprocal opposite signs