Nancyvarkey: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- |00:01 | Welcome to this tutorial on '''Graphing Lines simulation'''. |- |00:05 | In this tutorial, we will demonstrate '''Gr..."

2022-08-12T10:05:50Z

Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- |00:01 | Welcome to this tutorial on '''Graphing Lines simulation'''. |- |00:05 | In this tutorial, we will demonstrate '''Gr..."

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{|border=1
||'''Time'''
||'''Narration'''

|-
|00:01
| Welcome to this tutorial on '''Graphing Lines simulation'''.

|-
|00:05
| In this tutorial, we will demonstrate '''Graphing Lines''', an interactive '''PhET simulation'''.

|-
|00:12
| To follow this tutorial, learner should be familiar with topics in high school mathematics.

|-
|00:20
| Here I am using:

'''Ubuntu Linux OS''' version 14.04

'''Java''' version 1.7

'''Firefox Web Browser''' version 53.02.2

|-
|00:35
| Using this simulation, we will learn:

1. About Cartesian coordinate system

2. How to calculate the '''slope''' of a graphed line

3. To '''save''' the plotted lines

|-
|00:48
|4. How to change the '''slope''' and '''intercept''' of the line

5. How changing '''variable'''s in a '''linear''' equation will affect the line.

|-
|00:58
| An equation with two variables x and y is a linear equation. y=mx+b Here, '''m''' is '''slope''' of the line and '''b''' is '''intercept'''.

|-
|01:12
| Slope signifies rate of change of '''y''' value with respect to '''x''' value. '''y-intercept''' is y value when x=0.

|-
|01:26
| Let us begin the demonstration.

|-
|01:29
| Use the given '''link''' to download the '''simulation'''.

|-
|01:33
| I have already downloaded '''Graphing Lines simulation ''' to my '''Downloads''' folder.

|-
|01:39
| To open the simulation, right-click on '''graphing-lines_en.html''' file.

Select the option '''Open With Firefox Web Browser'''. File opens in the browser.

|-
|01:53
| This is the '''interface''' of '''Graphing Lines''' simulation.

|-
|01:57
|The interface has four '''screen'''s-'''Slope, Slope-Intercept, Point-Slope''' and
'''Line Game'''.

|-
|02:06
| Click on '''Slope''' screen.

|-
|02:10
|Screen has a '''Cartesian coordinate system''' with '''x''' and '''y''' axes.

|-
|02:16
| On the right side, formula box shows formula to find slope of the line.

|-
|02:23
|To calculate the slope, we can input values for '''y2, y1''' and '''x2, x1'''.

|-
|02:31
| Default values of y2, y1 are 4 and 2, and x2, x1 are 3 and 1.

|-
|02:41
| A graph is plotted using the default values. Here we can see '''Slope is 1'''.

|-
|02:49
| We can change the values of y2, y1 and x2, x1 using up and down arrow buttons.

|-
|02:57
| Plotted line can be saved using '''Save Line''' button.

|-
|03:02
|We can hide the formula box by clicking on red minus sign. To show the box, click on green plus button.

|-
|03:11
| Below the formula box, we have '''Slope''', '''Hide lines''' and '''Hide grid''' check boxes.

|-
|03:19
| If we click on '''Hide lines''' and '''Hide grid''' check-boxes, '''graph''' and '''grid''' are hidden.
Automatically '''Slope''' check-box is disabled.

|-
|03:32
|Let's uncheck '''Hide lines''' and '''Hide grid''' check boxes to enable '''Slope''' check box.

|-
|03:40
| Notice that graph displays value of the slope.
Observe that on moving purple and yellow points, x1, y1 and x2, y2 values can be changed.

|-
|03:54
|As we move the points, slope of the line changes.
Observe the change in values of x and y in the formula box.

|-
|04:04
| At the bottom of the screen, we have gray boxes to display coordinates of a point. These gray boxes are called as '''Point''' tools.

|-
|04:14
|Drag and place '''Point''' tools on purple and yellow points to see the coordinates.

|-
|04:20
|Drag the '''Point''' tools to the bottom.

|-
|04:24
| Drag the purple point to coincide with origin (0, 0).
Drag one of the '''Point''' tool and place it on the origin.

|-
|04:33
|Drag yellow point to coincide with (5,5). Observe that slope of the line is 1.

|-
|04:42
| Click on '''Save Line''' button in the formula box. Line is saved.

|-
|04:49
| Drag the yellow point to (2,8).
Drag the '''point''' tool and place it on yellow point.
This confirms that yellow point is at(2,8).

|-
|05:02
|Now '''Slope is 4.'''

|-
|05:05
| Click on '''Save Line''' in the formula box. Line is saved.

|-
|05:11
| Drag the yellow point to (-5,5). Drag and place '''Point''' tool on yellow point.

|-
|05:19
|Now '''Slope is -1'''.

|-
|05:22
|Click on '''Save Line''' in the formula box. Line is saved.

|-
|05:28
|Drag the '''point''' tool back to place. Drag the yellow point to (-2,8).

|-
|05:36
|Here '''Slope is -4'''.

|-
|05:39
| Click on '''Save Line'''. Line is saved.

|-
|05:44
| We have drawn 4 lines with different slopes. Notice that steepness is related to slope.

|-
|05:53
| As an assignment:

1. Find when slope is zero and when it is undefined.

2. Give an explanation.

|-
|06:04
| Now, let us explore '''Slope-Intercept''' screen at the bottom of the interface.

|-
|06:10
||Click on '''Slope-Intercept''' screen. Screen opens with a line y= 2/3x+1 (2 by 3 x plus 1).
|-
|06:21
|Here '''intercept''' value is 1.

|-
|06:25
| In this '''screen''', we can change the values of 'm' and 'b'.

|-
|06:30
| Drag the purple point on y-axis. Notice that purple point represents the intercept.
When we move the purple point, intercept for the line changes.

|-
|06:44
| The blue point is free to move across the graph.
When we move the blue point, slope of the line changes.

|-
|06:53
| Click on '''Reset''' button to reset the simulation.
Click on '''Save Line'''. Line is saved.

|-
|07:02
|Change the numerator value of '''m''' from 2 to 3 in the formula box.
Notice that slope is 1 while '''Intercept''' still remains 1.

|-
|07:14
| Now adjust '''m''' again to 2/3 and increase b value to 4.

Notice that the new line is parallel to the first line but intercepts y-axis at 4.

|-
|07:31
| Click on '''Save Line'''. Line is saved.

|-
|07:35
| Change '''b''' value to -2, click on '''Save Line'''. Line is saved.

|-
|07:43
|We have 3 parallel lines intercepting y-axis at 3 different points.

|-
|07:50
| Click on '''Reset''' button to reset the simulation.

|-
|07:55
|Let us change '''b''' value to zero. Notice that purple point is at the origin.

|-
|08:03
|Line now passes through the origin.

|-
|08:06
|Click on '''y=x''' and '''y=-x''' check boxes below the slope.

Notice that we have three lines passing through the origin.

|-
|08:19
| Now, let us now move on to '''Point-Slope''' screen.

|-
|08:23
| Click on '''Point-Slope''' at the bottom of the interface.

|-
|08:28
|In '''Point-Slope''' screen, a set of (x,y) values are substituted in the equation.

In this method, x and y values are defined.

|-
|08:41
| For a given value of (x, y), '''m''' can be calculated using the formula, '''y-y1 = m(x-x1)'''

|-
| 08:53
|The Generic point '''(x1, y1)''' is represented by the purple point.

|-
|08:59
|Drag the '''Point''' tool to the purple point, to see its coordinates.

|-
|09:04
|Drag the '''Point''' tool back to its place.

|-
|09:07
| Drag the purple and blue points freely across the graph to modify the equation of the line.

Drag and place purple point to (5,0).

|-
|09:20
|Then drag the blue point to (5,5).

|-
|09:24
| Notice that line is parallel to y-axis and slope is undefined.

|-
|09:31
|Click on '''Save line'''. Line is saved.

|-
|09:35
|Drag the purple point along the x-axis.

Notice that '''Slope''' is undefined all along the x-axis.

|-
|09:45
|Now, let us move on to '''Line Game''' screen.

|-
|09:49
| Click on '''Line Game''' screen.

|-
|09:52
| '''Line Game''' screen has 6 difficulty levels to play.

These games will test the knowledge gained using this simulation.

|-
|10:02
|It has a '''Timer''' and '''Sound''' buttons at the bottom of the screen.

|-
|10:08
|Click on each game and explore.

|-
|10:20
| Lets summarize.

|-
|10:22
|In this tutorial, we have learnt about '''Graphing Lines''', an interactive '''PhET simulation'''.

|-
|10:29
| Using this simulation, we have learnt:

1. About Cartesian coordinate system with x and y axes.

2. How to calculate the slope of a graphed line.

3. To '''save''' the plotted lines

|-
|10:43
|4. How to change the slope and intercept of the line

|-
|10:47
|5. How changing variables in a '''linear''' equation will affect the line.

|-
|10:53
| As an assignment:

1. Using '''Slope-Intercept''' screen, find when the value of slope is 1.

2. Using '''Point-Slope''' screen, find in which quadrants slope is positive.

|-
|11:09
| The video at the following link summarizes the '''Spoken Tutorial''' project. Please download and watch it.

|-
|11:17
|The '''Spoken Tutorial''' Project team conducts workshops using spoken tutorials and
gives certificates on passing online tests. For more details, please write to us.

|-
|11:29
| Please post your timed queries in this forum.

|-
|11:32
| This project is partially funded by Pandit Madan Malaviya National Mission on Teachers and Teaching.

|-
|11:41
| Spoken Tutorial Project is funded by '''NMEICT, MHRD,''' Government of India. More information on this mission is available at this link.

|-
|11:53
| This tutorial is contributed by Spoken tutorial team, IIT Bombay. Thank you for joining.
|-
|}

PhET-Simulations-for-Mathematics/C2/Graphing-Lines/English-timed - Revision history

Nancyvarkey: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- |00:01 | Welcome to this tutorial on '''Graphing Lines simulation'''. |- |00:05 | In this tutorial, we will demonstrate '''Gr..."