Teacher

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Teachers note

• Slides 2-4 are optional of course. I thought it
  was a good problem to quickly review slope.
• Pacing 2 days

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There has got to be some measurable way to get
this aircraftto clear such obstacles. Discuss
how you might radio a pilot and tell him or her
how toadjust the slope of their flight path in
order to clear the mountain.
If the pilot doesnt 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.
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Fortunately, there is a way to measure a proper
slope to clear the obstacle.
We measure the change in height requiredand
divide that by the horizontal change required.
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(No Transcript)
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Slopes of Parallel Perpendicular Lines

• Unit 11 Notes

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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 ?.

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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 ?
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On the corner of your notes write down whether
each of the next few pairs of lines are parallel,
perpendicular, or neither.
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slope of line r slope of line s
These lines are parallel.
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2. slope of line t slope of line u
These lines are perpendicular.
does m1 m2 -1 ?
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3. slope of line t slope of line u
These lines are parallel.
the slopes are both 3/4
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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?
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5. slope of line t slope of line u 7
Perpendicular.
.
7
-1
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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
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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 y1 x2 y2
x1 y1 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.
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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
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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
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You try ?

• Are the following lines ll, ?, or neither?
• y 1/2x 3
• y 2x 4
• Neither

• Are the following lines ll, ?, or neither?
• 8y -2x 5
• y 4x 7
• y (-1/4)x (5/8)
• y 4x 7
• ?

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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
y -4x -4
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Assignment

• Day 1
• Blue workbook pg. 54 28-30, pg. 55 7-18
• Day 2
• Practice ws working w/ ll and ? lines