Difference between revisions of "PhET-Simulations-for-Mathematics/C2/Graphing-Lines/English-timed"

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Latest revision as of 15:35, 12 August 2022

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.

Contributors and Content Editors

Nancyvarkey