lines and slopes
DESCRIPTION
My math lesson plan.TRANSCRIPT
![Page 1: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/1.jpg)
![Page 2: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/2.jpg)
Lines and Slopes
Table of Contents
• Introduction
• Drawing a Line
- Graphing Points First
• Slope
- Calculating Slope
- Finding Those Slopes
![Page 3: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/3.jpg)
Introduction
John and his friend wants to catch flies with their tongues. Their tongues are going to go straight just how a line would. John begins to use his knowledge about lines to catch flies.
![Page 4: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/4.jpg)
Drawing a Line
When you are able to know two points on a line then you are able to find the rest of the line. John is going to draw a line through these points.
![Page 5: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/5.jpg)
John shifts his tongue to reach the two points and go right through them.
![Page 6: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/6.jpg)
John begins to draw arrows to show that the line goes on forever.
*make sure you use a ruler or something with a straight edge to ensure
that your line is straight.*
![Page 7: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/7.jpg)
Graphing Points First
When graphing a line you must use an equation. Take for example when graphing the line:
3x + y = 9 John would have to find the values x and y to make the equation true.
![Page 8: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/8.jpg)
He choices to have x value equal 2. Once John has the value x, he has to find y by substituting the value x=2 into the equation.
3x + y = 9
3(2) + y = 9
6 + y = 9
-6 =-6
Y = 3
![Page 9: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/9.jpg)
John realize that when x = 2, y = 3 which makes the equation true. Now
he graphs the point ( 2, 3)
(2, 3)
![Page 10: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/10.jpg)
John needs one more point before graphing the line. So he has to find another value for x and y. He makes y = 0. He substitutes the value of y = 0 into the original equation.
(Shown below)
3x + y = 9
3x + 0 = 9
3x = 9
3 3
X = 3
![Page 11: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/11.jpg)
Here John found that when y=0, x=3that makes the equation true. Now
graph the second point (3,0)
(2, 3)
(3, 0)
![Page 12: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/12.jpg)
Again John draws a line through the points and add the arrows. Then write the equation beside the line to label it.
(2, 3)
(3, 0)
3x + y = 9
![Page 13: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/13.jpg)
To be sure John understands how to graph a line. He graphs another equation:
y = 2x - 4
Y = 2x – 4
Y = 2(0) – 4
Y = 0 – 4
Y = -4
Again he has to find two points to graph the equation. He has to find the values for xand y to make sure the equation is true. For the first point he substitutes 0 for the variable x.
![Page 14: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/14.jpg)
When John value x = 0 then y = -4. He can now graph the point (0, -4).
(0, -4)
![Page 15: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/15.jpg)
For the second point he substitutes 1 for the variable x.
Y= 2x – 4
Y = 2(1) – 4
Y = 2 – 4
Y = -2
John value x = 1 then y = -2.
Now he can graph the second
point (1, -2).
(0, -4)
(1, -2)Y = 2x - 4
He draws the line through the
points and add the arrows. He
then labels the line with the
equation.
![Page 16: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/16.jpg)
SlopeWhen using slope we use it to measure a line’s
slant.Here is a picture with three different types of slopes.
The green line has the biggest slope and the red line has the smallest slope out of the three slopes.
There can even
be a negative
slope line and
that’s when the
lines point down
instead of up.
Ex. Shown to
the right
![Page 17: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/17.jpg)
Calculating the Slope
When calculating the slope John define the slope as the change in the y-coordinates divide by the change in the x-coordinates. Most people refer to it as the “rise over run”.
*The change in y-coordinate is
the “rise” and the change in the
x-coordinate is the “run”.*
![Page 18: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/18.jpg)
Slope Formula
Change in x-coordinate and change in my y-coordinate is put in a formula using the Greek letter delta ∆. This is an abbreviation for change.
∆ Y∆ X
When identifying our points, our first point (x1, y1) and the second point (x2, y2). John substitute these points in for the delta ∆.
Y2 –Y1
X2 – Y1M=M=
![Page 19: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/19.jpg)
Finding the Slope
John first have to locate the two points on the line. We notice that the line intersect at the y-axis. This is the first point (0, 4). When then find the second point on the line where the two gridlines cross. This is our second point (2, 1).
![Page 20: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/20.jpg)
Now that we have our points John plugs it into the slope equation to find the slope.
M = (y2 – y1)/ (x2 – x1)
M = (1 – 4) / (2 – 0)
M = -3 / 2
The slope is negative.
![Page 21: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/21.jpg)
Overall
John has taught us how to draw a line by graphing the points and calculating the slope. Know he and his friends can catch their flies.
![Page 22: Lines and Slopes](https://reader031.vdocuments.us/reader031/viewer/2022020715/5559caffd8b42a98208b47ca/html5/thumbnails/22.jpg)
Cited
This is the site where I found my lesson plan and some of my graphs.
• http://mathforum.org/cgraph/cslope/drawline.html
This is the site where I found some of my graphs.
• http://nghsapphysicsb.blogspot.com/2009/10/super-explanation-of-how-rolling.html