1. Slope
What You'll Learn
You will learn to find the slopes of lines and use slope to
identify parallel and perpendicular lines. ?
1 – 4

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. The steepness of a line is called the _____. slope
Slope is defined as the ratio of the ____, or vertical change, to the ___, or horizontal change, as you move from one point on the line to another.
rise
run y x 10 -5
-10 5

6. The slope m of the non-vertical line passing through the points and isy x

7. The slope “m” of a line containing two points with coordinates
Definition of
Slope
The slope “m” of a line containing two points with coordinates
(x1, y1), and (x2, y2), is given by the formula

8. Slope
The slope m of a non-vertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. y x
(3, 6)
rise = = 5 units
(1, 1)
run = = 2 units ?
6 & 7

9. Y = 3x-2 3=3 so the lines are parallel
Slope
Postulate
4 – 3
Two distinct nonvertical lines are parallel iff they have _____________.
the same slope
Y = 3x+4
Y = 3x-2 3=3 so the lines are parallel

10. ? Y = 3x-2 Y = (-1/3) x +1 3* (1/3) = -1 so perpendicular
Slope
Postulate
4 – 4
Two nonvertical lines are perpendicular iff ___________________________.
the product of their slope is -1
Y = 3x-2
Y = (-1/3) x +1
3* (1/3) = -1 so perpendicular ?
8 & 9