1. Teacher’s note:
Slides 2-4 are optional of course. I thought it was a good problem to quickly review slope.
Pacing: 2 days

2. There has got to be some “measurable” way to get this aircraft to clear such obstacles.
Discuss how you might radio a pilot and tell him or her how to adjust the slope of their flight path in order to clear the mountain.
If the pilot doesn’t change something, he / she will not make it home for Christmas. Would you agree?
Consider the options:
1) Keep the same slope of his / her path.
Not a good choice!
2) Go straight up.
Not possible! This is an airplane, not a helicopter.

3. Fortunately, there is a way to measure a proper “slope” to clear the obstacle.
We measure the “change in height” required and divide that by the “horizontal change” required.

4. y x
10000

5. Slopes of Parallel & Perpendicular Lines
Unit 11 Notes

6. Rules for m of ll and  Lines
Slopes of ll lines are the same.
ll lines have equal slopes.
Any two vertical lines are ll.
Slopes of  lines are flipped and reversed.
Opposite reciprocals
Vertical & horizontal lines are .

7. If the lines are perpendicular then: m1 m2 = -1
So if the slope of the first line is 3/8, then
the slope of the second is ________
Just flip the first slope and change its sign 
3/8  -8/3 = -24/24 = -1 ✔

8. On the corner of your notes write down whether each of the next few pairs of lines are parallel, perpendicular, or neither.

9. slope of line r = slope of line s =
These lines are parallel.

10. 2. slope of line t = slope of line u =
These lines are perpendicular.
does m1 m2 = -1 ?

11. 3. slope of line t = slope of line u =
These lines are parallel.
the slopes are both 3/4

12. 4. slope of line t = slope of line u =
NEITHER!! Slopes are not congruent or opposite reciprocals of each other.
Do the two slopes multiply to
make -1?

13. 5. slope of line t = slope of line u = 7
Perpendicular. . 7
= -1

14. Example 1: Are the following lines parallel?
4y – 12x = 20
y = 3x – 1
Put them both in y-intercept form
y = mx + b
See if their slopes are the same, if so then they are ll.
y = -3x + 1
Slopes are equal, so the lines are ll.
-4y – 12x = 20
-4y = 12x + 20
y =-3x + 5

15. Example 2:
Line r contains points P(0,3) & Q(-2,5). Line t contains points R(0,-7) & S(3, -10). Are they ll, , or neither?
x1 y x2 y2
x1 y x2 y2
(0, 3) and (-2, 5)
m = (y2 – y1)/(x2 – x1)
= (5 – 3)/(-2 – 0)
= 2/-2
= -1
(0, -7) and (3, -10)
m = (y2 – y1)/(x2 – x1)
= (-10 – (-7))/(3 - 0)
= -3/3
= -1
Slopes are equal so the lines are ll.

16. Example 3:
Write an equation in point – slope form for the line parallel to 6x – 3y = 9 that contains point (-5, -8).
Step 1: Find the slope of the given line.
6x – 3y = 9
-3y = -6x + 9
y = 2x - 3
y – y1 = m(x – x1)
y – (-8) = 2(x – (-5))
y + 8 = 2x + 10
y = 2x + 2
Plug 2 in for m in the formula & plug in the point.
(-5, -8)
x1 y1

17. Example 4:
Write an equation for the line  to 3x + y = -5 that contains the point (-3, 7).
Step 2: Plug in your m and the point.
(-3, 7)
y – y1 = m(x – x1)
y – 7 = 1/3(x – (-3))
y – 7 = (1/3)x + 1
y = (1/3)x + 8
Step 1: Find slope of given line then flip and reverse it.
3x + y = -5
y = -3x – 5
m = -3
m = 1/3
x1 y1

18. You try  Are the following lines ll, , or neither? y = 1/2x + 3

19. 3) Write an equation of the line perpendicular to the graph of
YOU Try More 
1) Write an equation of the line parallel to the graph of y = 2x – 5 that passes through the point (3, 7).
y = 2x + 1
2) Write an equation of the line parallel to the graph of 3x + y = 6 that passes through the point (1, 4).
y = -3x + 7
3) Write an equation of the line perpendicular to the graph of
that passes through the point ( - 3, 8).
y = -4x -4

20. Assignment: Day 1 Blue workbook: pg. 54 #28-30, pg. 55 #7-18 Day 2
Practice ws “working w/ ll and  lines”