PhET/C2/Graphing-Lines/English-timed
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 variables 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 screens-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. |