2. Slopes of Parallel and Perpendicular Lines Objective: To discover the relationships between the slopes of parallel lines and perpendicular lines.

3. What type of lines do lines “p” and “q” look like?

4. Answer p and q appear to be parallel lines! How can we use mathematics to be sure they are indeed parallel?

5. Calculate the slope of each.

6. slope of p = slope of q = =

7. What do you notice about the slopes of these two lines? The slopes are congruent. parallel congruent

8. Parallel Conjucture: Two lines are parallel if their slopes are equal. Recall the definition of parallel lines then write a few sentences describing why it makes sense that parallel lines would have equal slopes.

9. Are these lines parallel? slope a = - slope b = - NO –The slopes are not 

10. Are these lines parallel? slope c = slope d = = YES – Slopes are 

11. You will be shown the slopes of two lines. Write down whether each pair of lines are parallel or not.

12. 1.slope of line r = slope of line s = These lines are parallel.

13. 3. slope of line t = slope of line u = These lines are parallel.

14. 4. slope of line t = slope of line u = Not parallel because the slopes are not congruent to each other.

15. Ex. Determine whether the graphs of y = -3x + 4 and 6x + 2y = -10 are parallel lines. Step 1: make both equations in the y-intercept form to compare slopes 6x + 2y = -10 can be changed to y-intercept form by solving for y

16. 6x + 2y = -10 -6x 2y = -6x -10 2 2 2 y = -3x - 5 Subtract 6x Divide by 2

17. Step 2: compare the slopes of both equations. The first equation y = -3x + 4 has a slope of -3 and the second equation has the same slope of -3 Therefore, the graph of the lines will be parallel.

18. Practice: Determine whether the graphs are parallel lines (without graphing) 1) 3x - y = -5 and 5y -15x = 10 2) 4y = -12x + 16 and y = 3x + 4