EXPLORING Mountains have slopes…. …and so do lines.
-
Upload
toby-obrien -
Category
Documents
-
view
220 -
download
0
Transcript of EXPLORING Mountains have slopes…. …and so do lines.
![Page 1: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/1.jpg)
EXPLORING
![Page 2: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/2.jpg)
Mountains have slopes….
![Page 3: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/3.jpg)
…and so do lines.
![Page 4: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/4.jpg)
A skier can go down this slope
![Page 5: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/5.jpg)
When you think of down, you think of negative.
This line, like the mountain, has a
negative slope
![Page 6: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/6.jpg)
You can also run up the mountain.
![Page 7: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/7.jpg)
When you think of up, you think positive.
This lin
e, like th
e mounta
in, has a
posit
ive
slope.
![Page 8: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/8.jpg)
Does this mountain have a slope??
Slope?? This haszero slope!
![Page 9: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/9.jpg)
Horizontal lines have a slope of zero.
000
![Page 10: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/10.jpg)
What do you think the slope of a vertical line would be ??
This is not a slope; it’s a cliff!
The slope of a vertical
line is undefined!
It has NO slope.
![Page 11: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/11.jpg)
A line that goes down from left to right has what kind of slope???
![Page 12: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/12.jpg)
A line that goes up from left to right has what kind of slope???
![Page 13: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/13.jpg)
What kind of line has a slope of zero??
![Page 14: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/14.jpg)
What is the slope of this line??
![Page 15: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/15.jpg)
One more time….
+
-
0
undefined
![Page 16: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/16.jpg)
+-0
undefined
Matching.a.
b.
c.
d.
![Page 17: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/17.jpg)
Determining the Value of a Slope
![Page 18: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/18.jpg)
Now that you can identify whether a line has a positive or negative slope,
let’s learn how to determine the value of the slope.
This line has a slope
of 1.
How do you figure that
out?
![Page 19: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/19.jpg)
First, a few facts about slope.
Slope is the ratio of the
change in y to the change in x.
Vertical change : y _______________
Horizontal change : x
Or in easy terms, it is RISE divided by RUN.
RISE
RUN
Slope is always represented by the letter m
![Page 20: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/20.jpg)
Look at your line and identify two points between which you can determine the
slope.What is the rise?
up 2
What is the run?
over 2
This gives you the ratio:
2 12=
![Page 21: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/21.jpg)
Let’s try another one.
Choose two points.Count your rise.
up 2Count your run.
over 3
So the slope is:
23
![Page 22: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/22.jpg)
This one is a little different.
Choose two points.Count your rise.
up 1 Up 1 or +1
Count your run.
back 2
Back 2 or -2
The slope is:
=12
- 12
-
![Page 23: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/23.jpg)
To summarize…
If you can count, you can find the slope.
1. Choose two points on the line.
2. Count from the lower point in a vertical direction to where the upper point is.3. Count right or left to the second point.4. The slope is the RISE (first distance) divided by the RUN (second distance).
![Page 24: EXPLORING Mountains have slopes…. …and so do lines.](https://reader035.fdocuments.net/reader035/viewer/2022062409/5697bf781a28abf838c81e92/html5/thumbnails/24.jpg)
Now it’s time for you to practice what you
have learned!