slope of a line
DESCRIPTION
microlesson,math,slope, line,math project,TRANSCRIPT
![Page 1: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/1.jpg)
FINDING POOKY
Mission Impossible:
Garfield in
![Page 2: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/2.jpg)
![Page 3: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/3.jpg)
It was a typical Monday for Garfield.
![Page 4: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/4.jpg)
He slept all day long, dreaming of him
![Page 5: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/5.jpg)
in a carnival with Pooky, his bestfriend toy.
![Page 6: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/6.jpg)
![Page 7: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/7.jpg)
That was the best rollercoaster ride
ever!
![Page 8: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/8.jpg)
Hmm.. I wonder where Pooky is.
![Page 9: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/9.jpg)
Maybe I left him on the bed again.
![Page 10: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/10.jpg)
![Page 11: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/11.jpg)
Where’s Pooookkkyyyy?! I left him on my bed
and now he’s gone!
![Page 12: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/12.jpg)
I knew it! That Odie is making fun out of me. And he left a letter. How
sweet!
![Page 13: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/13.jpg)
He said that the only way I could
get Pooky back is to play his game.
Darn!
CLick here to open the letter
![Page 14: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/14.jpg)
What’s up pussy?! Wanna play a game? I got one and it is starting now. I got your Pooky. Let me give you a clue on how to get to my next love letter that will tell where Pooky is. But you gotta need some Mathematics skills. Here’s the first clue:
![Page 15: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/15.jpg)
Here are two points in a linear function. Its slope will tell you the number of steps you must take, 53O east of south from your bedroom. You better get the answer fast or else you wouldn’t get Pooky back!
(-7,18), (-10, -12)
(Click the paw print to return to Garfield)
![Page 16: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/16.jpg)
Hmmm… that was quite difficult. But I think I can solve it.
![Page 17: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/17.jpg)
Slope? What’s a slope? Aahhh yes! It’s the lesson Mr. De Guzman taught last week.
![Page 18: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/18.jpg)
He said that we should use this formula in solving it.
![Page 19: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/19.jpg)
First, determine y2, y1, x2 and x1 in (-
7,18), (-10, -12) then place the values in
to get m or the slope.
![Page 20: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/20.jpg)
In(-7,18), (-10,-12) y2
and y1 is the y-coordinates of the second and first
ordered pairs respectively, which
are -12 and 18.
![Page 21: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/21.jpg)
And the x2 and x1 are the x-coordinates of the second and first
ordered pairs respectively, which
are -10 and 7.
![Page 22: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/22.jpg)
That’s it! Therefore, the slope is
10!
![Page 23: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/23.jpg)
That means I should take 10 steps from my
room, 53O east of south.
![Page 24: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/24.jpg)
From the room, take 10 steps to
the southeast!
![Page 25: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/25.jpg)
Here it is! Another love letter from my dear best friend. Oh! How sweet of him!
Click here to open
the second letter
![Page 26: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/26.jpg)
Congrats Pussy! You’ve got the first clue. So now is the time for the next one.
Here’s a graph of a linear equation. Its rise and run will tell the number of steps you’ll take from here. Good luck!
![Page 27: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/27.jpg)
(Click the paw print to return to Garfield)
![Page 28: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/28.jpg)
Uhhh… A graph?! It’s more difficult than the first task. But I’m pretty sure I can solve this.
![Page 29: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/29.jpg)
![Page 30: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/30.jpg)
The length of those broken lines is equal to the steps I’ll take. It is also the rise and the run or the slope.
![Page 31: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/31.jpg)
To get the slope, I need to determine two points on the line. And by observation, we can see that (-7,5) and (0,7) are on the line.
![Page 32: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/32.jpg)
We now have two points and we can solve the rise and run.
The slope is also known as the rise over run so the rise is 5 and run is 14.
-
![Page 33: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/33.jpg)
That means I have to take 14 steps to the South (because of the negative sign) and 5 steps to the east. But due to the house’s design, I need to take the eastward steps first.
![Page 34: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/34.jpg)
5 steps to the East
then 14 steps to
the south.
![Page 35: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/35.jpg)
Oh yeah! I’m so close to finding Pooky. Let’s read Odie’s last love letter for me.
Click here to openthe last letter
![Page 36: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/36.jpg)
Great job, little pussy. You have done the first two clues and now here’s the last clue. Consider the linear equation below. Its slope is the number of eastward steps you’ll take from here. I’M WISHING YOU A LOT OF LUCK!
(Click the paw print to return to Garfield)
0=-16X+2Y
![Page 37: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/37.jpg)
This is an easy one! In an equation, we can solve for the slope by using –a/b! Piece of cake!
![Page 38: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/38.jpg)
In the equation 0=-16X+2Y, -16 is A and 2 is B. By using –A/B, we get 8 as the slope. Eureka!
![Page 39: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/39.jpg)
Which means 8 steps to the east!
![Page 40: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/40.jpg)
![Page 41: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/41.jpg)
Garfield has reached the place where Odie is waiting.
Hey Odie! I’ve solved all of your challenges.
Enough already! Where’s Pooky?
Alright! Chill! You know that I was just messing with you.
You’re good. Since you have solved all my challenges, here, take
your Pooky back.
![Page 42: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/42.jpg)
I’m sorry,
Garfield. I
promise to never
ever ever take
Pooky again.
Awww. It’s ok, my friend. To be honest with you, I
enjoyed your silly prank.
Click to retrieve Pooky
![Page 43: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/43.jpg)
MISSIONACCOMPLISHED!
![Page 44: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/44.jpg)
![Page 45: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/45.jpg)
Kids, let me discuss
SLOPE OF A LINEAR
FUNCTION
![Page 46: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/46.jpg)
In mathematics, the slope or gradient of a line
describes its steepness, incline, or grade.
![Page 47: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/47.jpg)
It is the constant rate of change of a linear function.
![Page 48: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/48.jpg)
It can be though of as the ratio of the vertical change
to the horizontal change between two points on the
graph of a line.
![Page 49: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/49.jpg)
If the two points are (x1, y1) and (x2, y2), then the vertical change is y2 - y1
and the horizontal change is x2 - x1.
![Page 50: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/50.jpg)
Hence, we use the formula
![Page 51: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/51.jpg)
Graph of f(x) = mx + b
Positive Slope(the line rises
from left to right)
![Page 52: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/52.jpg)
Graph of f(x) = -mx + b
Negative Slope(the line falls
from left to right)
![Page 53: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/53.jpg)
Graph of f(x) = b
Zero Slope(horizontal line; passes
through the y-axis)
![Page 54: slope of a line](https://reader038.vdocuments.net/reader038/viewer/2022103116/55895c04d8b42a543f8b457e/html5/thumbnails/54.jpg)
SUBMITTED TO: Mr. Eric De Guzman
SUBMITTED BY:John Francis P. GonzagaEmmanuel Gabrielle M. RiveraMary Grace M. Lopez(IV-Diamond, S.Y. 2012-2013)
Copyright 2012
Credits to the maker of Garfield the Movie and Garfield Comics