Difference between revisions of "PhET/C2/Graphing-Lines/English"

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(Created page with "{|border=1 ||'''Visual Cue''' ||'''Narration''' |- || '''Slide Number 1''' '''Title Slide''' || Welcome to this tutorial on '''Graphing Lines simulation'''. |- || '''Sl...")
 
Line 84: Line 84:
 
'''Link for PhET simulation'''  
 
'''Link for PhET simulation'''  
  
−
[http://phet.colorado.edu/ http://phet.colorado.edu]  
+
[http://phet.colorado.edu/]  
 
|| Use the given link to download the simulation.  
 
|| Use the given link to download the simulation.  
  
Line 129: Line 129:
 
|| Point to the formula box  
 
|| Point to the formula box  
  
−
point to the input buttons.  
+
 
 +
|| On the right side, formula box shows formula to find slope of the line.
 +
|-
 +
||point to the input buttons.  
  
 
Point to the default values.  
 
Point to the default values.  
  
−
Point to the graph and slope.
+
||To calculate the slope, we can input values for y2, y1 and x2, x1.  
−
|| On the right side, formula box shows formula to find slope of the line.
+
−
 
+
−
To calculate the slope, we can input values for y2, y1 and x2, x1.  
+
  
 
Default values of y2, y1 are 4 and 2.  
 
Default values of y2, y1 are 4 and 2.  
  
 
And x2, x1 are 3 and 1.  
 
And x2, x1 are 3 and 1.  
−
 
+
|-
−
A graph is plotted using the default values.  
+
||Point to the graph and slope.
 +
||A graph is plotted using the default values.  
  
 
Here we can see, '''Slope is 1'''.  
 
Here we can see, '''Slope is 1'''.  
Line 150: Line 151:
 
|| We can change the values of y2, y1 and x2, x1 using up and down arrow buttons.  
 
|| We can change the values of y2, y1 and x2, x1 using up and down arrow buttons.  
 
|-  
 
|-  
−
|| Point to the '''Save Line''' option  
+
|| Point to the '''Save Line''' option
  
−
point to '''Erase Lines''' option.  
+
Point to '''Erase Lines''' option.
−
 
+
|| Plotted line can be saved using '''Save Line''' button.
−
Click on the red minus sign.  
+
|-
 +
||Click on the red minus sign.  
  
 
Click on green plus button.  
 
Click on green plus button.  
−
|| Plotted line can be saved using '''Save Line''' button.
+
||We can hide the formula box, by clicking on red minus sign.  
−
 
+
−
We can hide the formula box, by clicking on red minus sign.  
+
  
 
To show the box click on green plus button.  
 
To show the box click on green plus button.  
Line 170: Line 170:
 
|| Point to the check boxes.  
 
|| Point to the check boxes.  
  
−
Uncheck, Hide lines and Hide grid check boxes
 
 
|| If we click on, '''Hide lines''' and '''Hide grid''' check boxes, graph and grid are hidden.  
 
|| If we click on, '''Hide lines''' and '''Hide grid''' check boxes, graph and grid are hidden.  
  
 
Automatically, '''Slope''' check box is disabled.  
 
Automatically, '''Slope''' check box is disabled.  
−
 
+
|-
−
Let's uncheck '''Hide lines''' and '''Hide grid''' check boxes to enable '''Slope''' check box.  
+
||Uncheck, Hide lines and Hide grid check boxes
 +
||Let's uncheck '''Hide lines''' and '''Hide grid''' check boxes to enable '''Slope''' check box.  
  
 
|-  
 
|-  
 
|| Point to the Graph and slope.  
 
|| Point to the Graph and slope.  
 +
|| 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.
 +
|-
 +
||
 
Point to purple and yellow points on the line.  
 
Point to purple and yellow points on the line.  
  
 
Click and drag them on the line.  
 
Click and drag them on the line.  
−
 
+
||As we move the points, slope of the line changes.  
−
|| 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.
+
−
 
+
−
As we move the points, slope of the line changes.  
+
  
 
Observe the change in values of x and y in the formula box.  
 
Observe the change in values of x and y in the formula box.  
Line 196: Line 195:
  
  
−
Drag and place the '''Point''' tools on purple and yellow points.
 
−
 
−
Point to the coordinates.
 
 
|| At the bottom of the screen, we have gray boxes to display coordinates of a point.  
 
|| At the bottom of the screen, we have gray boxes to display coordinates of a point.  
  
 
These gray boxes are called as '''Point''' tools.  
 
These gray boxes are called as '''Point''' tools.  
 +
|-
 +
||Drag and place the '''Point''' tools on purple and yellow points.
  
−
Drag and place '''Point''' tools on purple and yellow points to see the coordinates.  
+
Point to the coordinates.
−
 
+
||Drag and place '''Point''' tools on purple and yellow points to see the coordinates.  
−
Drag the '''Point''' tools to the bottom.  
+
|-
 +
||Drag the '''Point''' tools
 +
||Drag the '''Point''' tools to the bottom.  
 
   
 
   
 
|-  
 
|-  
−
|| Drag the points.  
+
|| Drag the purple point.
  
−
Point to slope.
+
Drag one of the '''Point''' tool
 
|| Drag the purple point to coincide with origin (0, 0).  
 
|| Drag the purple point to coincide with origin (0, 0).  
  
 
Drag one of the '''Point''' tool and place it on the origin.  
 
Drag one of the '''Point''' tool and place it on the origin.  
 +
|-
 +
||Drag yellow point
  
−
Drag yellow point to coincide with (5,5).  
+
Point to slope.
 +
||Drag yellow point to coincide with (5,5).  
  
 
Observe that slope of the line is 1.  
 
Observe that slope of the line is 1.  
Line 234: Line 237:
  
 
This confirms that yellow point is at(2,8).  
 
This confirms that yellow point is at(2,8).  
−
 
+
|-
−
Now '''Slope is 4.'''  
+
||Point to Slope
 +
||Now '''Slope is 4.'''  
  
 
|-  
 
|-  
Line 250: Line 254:
  
 
Drag and place Point tool on yellow point.  
 
Drag and place Point tool on yellow point.  
−
 
+
|-
−
Now '''Slope is -1'''.  
+
||Point to Slope
 +
||Now '''Slope is -1'''.  
  
 
|-  
 
|-  
Line 266: Line 271:
  
 
Drag the yellow point to (-2,8).  
 
Drag the yellow point to (-2,8).  
−
 
+
|-
−
Here '''Sope is -4'''.  
+
||Point to Slope
 +
||Here '''Slope is -4'''.  
  
 
|-  
 
|-  
−
|| Click '''Save Line.'''  
+
|| Click '''Save Line'''.
−
|| Click on '''Save Line.'''  
+
|| Click on '''Save Line'''.
  
 
Line is saved  
 
Line is saved  
Line 289: Line 295:
 
Give an explanation.  
 
Give an explanation.  
 
|-  
 
|-  
−
|| Point to '''Slope-Intercept''' screen.
+
|| Cursor on '''Slope-Intercept''' screen.
−
 
+
−
Click on '''Slope-Intercept''' screen.  
+
 
|| Now let us explore '''Slope-Intercept''' screen at the bottom of the interface.  
 
|| Now let us explore '''Slope-Intercept''' screen at the bottom of the interface.  
 +
|-
 +
||Click on '''Slope-Intercept''' screen.
  
−
Click on '''Slope-Intercept''' screen.  
+
Point to the line.
 +
||Click on '''Slope-Intercept''' screen.  
  
 
Screen opens with a line y= 2/3x+1.  
 
Screen opens with a line y= 2/3x+1.  
−
 
+
|-
−
Here intercept value is 1.  
+
||Point to intercept.
 +
||Here intercept value is 1.  
  
 
|-  
 
|-  
Line 333: Line 341:
 
Drag the '''Point''' tool to the blue point.  
 
Drag the '''Point''' tool to the blue point.  
  
−
Point to the intercept.  
+
Point to slope and intercept.  
 
|| Change the numerator value of '''m''' from 2 to 3 in the formula box.  
 
|| Change the numerator value of '''m''' from 2 to 3 in the formula box.  
  
Line 344: Line 352:
  
 
Click on '''Save Line'''  
 
Click on '''Save Line'''  
 +
 
|| Now adjust '''m''' again to 2/3 and increase b value to 4.  
 
|| Now adjust '''m''' again to 2/3 and increase b value to 4.  
  
Line 349: Line 358:
  
 
Click on '''Save Line'''.  
 
Click on '''Save Line'''.  
−
 
+
|-
−
Line is saved.  
+
||Point to saved line.
 +
||Line is saved.  
  
 
|-  
 
|-  
Line 357: Line 367:
 
Click on '''Save Line''' in the formula box.  
 
Click on '''Save Line''' in the formula box.  
  
−
Point to 3 parallel lines with different points.
+
 
 
|| Change '''b''' value to -2  
 
|| Change '''b''' value to -2  
  
Line 363: Line 373:
  
 
Line is saved.  
 
Line is saved.  
−
 
+
|-
−
We have 3 parallel lines intercepting y axis at 3 different points.  
+
||Point to 3 parallel lines with different points.
−
 
+
||We have 3 parallel lines intercepting y axis at 3 different points.  
 
|-  
 
|-  
 
|| Click on '''Reset''' button.  
 
|| Click on '''Reset''' button.  
 
|| Click on '''Reset''' button to reset the simulation.  
 
|| Click on '''Reset''' button to reset the simulation.  
−
 
 
|-  
 
|-  
 
|| Point to b value.  
 
|| Point to b value.  
Line 375: Line 384:
 
Point to the line.  
 
Point to the line.  
  
−
Point to the origin.
 
−
 
−
Click on '''y=x''' and '''y=-x''' check boxes.
 
−
 
−
Point to the lines.
 
 
|| Let us change b value to zero.  
 
|| Let us change b value to zero.  
  
 
Notice that purple point is at the origin.  
 
Notice that purple point is at the origin.  
 +
|-
 +
||Point to the origin.
 +
||Line now passes through the origin.
 +
|-
 +
||Click on '''y=x''' and '''y=-x''' check boxes.
  
−
Line now passes through the origin.  
+
Point to the lines.  
−
 
+
||Click on '''y=x''' and '''y=-x''' check boxes below the slope.  
−
Click on '''y=x''' and '''y=-x''' check boxes below the slope.  
+
  
 
Notice that we have three lines passing through the origin.  
 
Notice that we have three lines passing through the origin.  
Line 395: Line 403:
 
|-  
 
|-  
 
|| Click on '''Point-Slope''' at the bottom of the screen.  
 
|| Click on '''Point-Slope''' at the bottom of the screen.  
−
 
 
|| Click on '''Point-Slope''' at the bottom of the interface.  
 
|| Click on '''Point-Slope''' at the bottom of the interface.  
−
 
+
|-
−
In '''Point-Slope''' screen, a set of (x,y) values are substituted in the equation.  
+
||Cursor on the screen.
 +
||In '''Point-Slope''' screen, a set of (x,y) values are substituted in the equation.  
  
 
In this method, x and y values are defined.  
 
In this method, x and y values are defined.  
Line 405: Line 413:
 
|| point to the formula box.  
 
|| point to the formula box.  
  
−
Point to purple point and drag the point tool to see co-ordinates.
 
 
|| For a given value of (x, y), '''m''' can be calculated using the formula, '''y-y1 = m(x-x1)'''  
 
|| For a given value of (x, y), '''m''' can be calculated using the formula, '''y-y1 = m(x-x1)'''  
−
 
+
|-
−
the Generic point '''(x1,y1)''' is represented by the purple point.  
+
||Point to purple point and drag the point tool to see co-ordinates.
−
 
+
||The Generic point '''(x1,y1)''' is represented by the purple point.  
−
Drag the '''Point''' tool to the purple point to see the coordinates.  
+
|-
−
 
+
||Drag the '''Point''' tool to the purple point
−
Drag the '''Point''' tool back to its place.  
+
||Drag the '''Point''' tool to the purple point to see the coordinates.  
−
 
+
|-
 +
||Drag the '''Point''' tool back to its place.  
 +
||Drag the '''Point''' tool back to its place.
 
|-  
 
|-  
 
|| Demonstrate moving line.  
 
|| Demonstrate moving line.  
Line 421: Line 430:
  
 
Drag and place purple point to (5,0).  
 
Drag and place purple point to (5,0).  
−
 
+
|-
−
Then drag the blue point to (5,5).  
+
||Drag the blue point to (5,5).
−
 
+
||Then drag the blue point to (5,5).  
 
|-  
 
|-  
 
|| Point to y-axis and slope.  
 
|| Point to y-axis and slope.  
−
 
−
Click on '''Save line'''.
 
 
|| Notice that line is parallel to y-axis and slope is undefined.  
 
|| Notice that line is parallel to y-axis and slope is undefined.  
 +
|-
 +
||Click on '''Save line'''.
 +
||Click on '''Save line'''. Line is saved.
 +
|-
 +
||Drag the purple point along the x-axis.
  
−
Click on '''Save line'''. Line is saved.
+
Point to  '''Slope''' .
−
 
+
||Drag the purple point along the x-axis.  
−
Drag the purple point along the x-axis.  
+
  
 
Notice that '''Slope''' is undefined all along the x-axis.  
 
Notice that '''Slope''' is undefined all along the x-axis.  
−
 
 
|-  
 
|-  
−
||  
+
|| move the cursor to '''Game''' screen.
 
|| Now let us move on to '''Game''' screen.  
 
|| Now let us move on to '''Game''' screen.  
  
 
|-  
 
|-  
 
|| Go to '''Line Game''' tab  
 
|| Go to '''Line Game''' tab  
 +
 +
Point to the levels.
 
|| Click on '''Line Game''' screen.  
 
|| Click on '''Line Game''' screen.  
  
Line 447: Line 459:
  
 
These games will test the knowledge gained using this simulation.  
 
These games will test the knowledge gained using this simulation.  
−
 
+
|-
−
It has a '''Timer''' and '''Sound''' buttons at the bottom of the screen.  
+
||Point to '''Timer''' and '''Sound''' buttons
−
 
+
||It has a '''Timer''' and '''Sound''' buttons at the bottom of the screen.  
−
Click on each game and explore.  
+
|-
 +
||Click on each game >> explore.
 +
||Click on each game and explore.  
  
 
|-  
 
|-  
−
|| '''Slide Number 8'''  
+
|| '''Slide Number 9'''  
  
 
'''Summary'''  
 
'''Summary'''  
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|-  
 
|-  
−
|| '''Slide Number 9'''  
+
|| '''Slide Number 10'''  
  
 
'''Summary'''  
 
'''Summary'''  
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How changing variables in a linear equation will affect the line.  
 
How changing variables in a linear equation will affect the line.  
 
|-  
 
|-  
−
|| '''Slide Number 10'''  
+
|| '''Slide Number 11'''  
 
|| As an assignment  
 
|| As an assignment  
  
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|-  
 
|-  
−
|| '''Slide Number 11'''  
+
|| '''Slide Number 12'''  
  
 
'''About the Spoken Tutorial Project'''  
 
'''About the Spoken Tutorial Project'''  
Line 496: Line 510:
  
 
|-  
 
|-  
−
|| '''Slide Number 12'''  
+
|| '''Slide Number 13'''  
  
 
'''Spoken Tutorial workshops'''  
 
'''Spoken Tutorial workshops'''  
Line 507: Line 521:
 
For more details, please write to us.  
 
For more details, please write to us.  
 
|-  
 
|-  
−
|| '''Slide Number 13'''  
+
|| '''Slide Number 14'''  
  
 
'''Forum for specific questions:'''  
 
'''Forum for specific questions:'''  
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|-  
 
|-  
−
|| '''Slide Number 14'''  
+
|| '''Slide Number 15'''  
  
 
'''Acknowledgement'''  
 
'''Acknowledgement'''  
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|-  
 
|-  
−
|| '''Slide Number 15'''  
+
|| '''Slide Number 16'''  
  
 
'''Acknowledgement'''
 
'''Acknowledgement'''

Revision as of 15:51, 8 January 2018

Visual Cue Narration
Slide Number 1

Title Slide

Welcome to this tutorial on Graphing Lines simulation.
Slide Number 2

Learning Objectives

Demonstrate an interactive PhET simulation, Graphing Lines

In this tutorial, we will demonstrate, Graphing Lines, an interactive PhET simulation.
Slide Number 3

Pre-requisites

To follow this tutorial,

Learner should be familiar with topics in high school mathematics.

Slide Number 4

System Requirements

Ubuntu Linux OS version 14.04

Java version 1.7.0

Firefox Web Browser 53. 02.2

Here I am using,

Ubuntu Linux OS version 14.04

Java version 1.7

Firefox Web Browser version 53.02.2

Slide Number 5

Learning Goals

Using this simulation we will learn,

About Cartesian coordinate system

How to calculate the slope of a graphed line

To save the plotted lines

How to change the slope and intercept of the line

How, changing variables in a linear equation will affect the line.

Slide Number 6

Linear Equation

y=mx+b

point to m and b.

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.

Slope signifies rate of change of y value with respect to x value.

y-intercept is y value when x=0

Let us begin the demonstration.
Slide Number 7

Link for PhET simulation

[1]

Use the given link to download the simulation.
Point to the file in Downloads folder. I have already downloaded Graphing Lines simulation to my Downloads folder.
Right click on graphing-lines_en.html file.

Select Open With Firefox Web Browser option.

Point to the browser address.

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.

Cursor on the interface. This is the interface of Graphing Lines simulation.
Point to each screen. The interface has four screens,

Slope

Slope-Intercept

Point-Slope and

Line Game.

Click on Slope screen. Click on Slope screen.
Point to the graph. Screen has a Cartesian coordinate system with x and y axes.
Point to the formula box


On the right side, formula box shows formula to find slope of the line.
point to the input buttons.

Point to the default values.

To calculate the slope, we can input values for y2, y1 and x2, x1.

Default values of y2, y1 are 4 and 2.

And x2, x1 are 3 and 1.

Point to the graph and slope. A graph is plotted using the default values.

Here we can see, Slope is 1.

Point to the buttons. We can change the values of y2, y1 and x2, x1 using up and down arrow buttons.
Point to the Save Line option

Point to Erase Lines option.

Plotted line can be saved using Save Line button.
Click on the red minus sign.

Click on green plus button.

We can hide the formula box, by clicking on red minus sign.

To show the box click on green plus button.

Point to Slope, Hide lines, Hide grid check boxes. Below the formula box, we have Slope, Hide lines and Hide grid check boxes.
Point to the check boxes. If we click on, Hide lines and Hide grid check boxes, graph and grid are hidden.

Automatically, Slope check box is disabled.

Uncheck, Hide lines and Hide grid check boxes Let's uncheck Hide lines and Hide grid check boxes to enable Slope check box.
Point to the Graph and slope. 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.

Point to purple and yellow points on the line.

Click and drag them on the line.

As we move the points, slope of the line changes.

Observe the change in values of x and y in the formula box.

Point to the Point tools (gray boxes displaying point co-ordinates).


At the bottom of the screen, we have gray boxes to display coordinates of a point.

These gray boxes are called as Point tools.

Drag and place the Point tools on purple and yellow points.

Point to the coordinates.

Drag and place Point tools on purple and yellow points to see the coordinates.
Drag the Point tools Drag the Point tools to the bottom.
Drag the purple point.

Drag one of the Point tool

Drag the purple point to coincide with origin (0, 0).

Drag one of the Point tool and place it on the origin.

Drag yellow point

Point to slope.

Drag yellow point to coincide with (5,5).

Observe that slope of the line is 1.

Click on Save Line button. Click on Save Line button in the formula box.

Line is saved.

Drag the yellow point to (2,8).

Drag the point tool and place it on yellow point.

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).

Point to Slope Now Slope is 4.
Click on Save Line in right panel. Click on Save Line in the formula box.

Line is saved.

Drag the yellow point to (-5,5).

Drag the point tool.

Drag the yellow point to (-5,5).

Drag and place Point tool on yellow point.

Point to Slope Now Slope is -1.
Click on Save Line in right panel. Click on Save Line in the formula box.

Line is saved.

Drag the yellow point to (-2,8) x=-2, y=8

Point to the slope.

Drag the point tool back to place.

Drag the yellow point to (-2,8).

Point to Slope Here Slope is -4.
Click Save Line. Click on Save Line.

Line is saved

Notice the 6 lines in graph, on left panel. We have drawn 4 lines with different slopes.

Notice that steepness is related to slope.

Slide Number 8

Assignment

As an assignment,

Find when slope is zero and when it is undefined.

Give an explanation.

Cursor on Slope-Intercept screen. Now let us explore Slope-Intercept screen at the bottom of the interface.
Click on Slope-Intercept screen.

Point to the line.

Click on Slope-Intercept screen.

Screen opens with a line y= 2/3x+1.

Point to intercept. Here intercept value is 1.
Point to m and b. In this screen we can change the values of 'm' and 'b'.
Drag the purple point on the line.

Point to the intercept.

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.

Move the blue point on the line.

Point to the blue point.

The blue point is free to move across the graph.

When we move the blue point, slope of the line changes.

Click on Reset button.

Click on Save Line

Click on Reset button to reset the simulation.

Click on Save Line. Line is saved.

Change the value to 3.

Drag the Point tool to the blue point.

Point to slope and intercept.

Change the numerator value of m from 2 to 3 in the formula box.

Notice that slope is 1 while Intercept still remains 1.

Point the line.

Point to the intercept.

Click on Save Line

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.

Click on Save Line.

Point to saved line. Line is saved.
Point to the line.

Click on Save Line in the formula box.


Change b value to -2

Click on Save Line.

Line is saved.

Point to 3 parallel lines with different points. We have 3 parallel lines intercepting y axis at 3 different points.
Click on Reset button. Click on Reset button to reset the simulation.
Point to b value.

Point to the line.

Let us change b value to zero.

Notice that purple point is at the origin.

Point to the origin. Line now passes through the origin.
Click on y=x and y=-x check boxes.

Point to the lines.

Click on y=x and y=-x check boxes below the slope.

Notice that we have three lines passing through the origin.

Point to Point-Slope screen. Let us now move on to Point-Slope screen.
Click on Point-Slope at the bottom of the screen. Click on Point-Slope at the bottom of the interface.
Cursor on the screen. In Point-Slope screen, a set of (x,y) values are substituted in the equation.

In this method, x and y values are defined.

point to the formula box. For a given value of (x, y), m can be calculated using the formula, y-y1 = m(x-x1)
Point to purple point and drag the point tool to see co-ordinates. The Generic point (x1,y1) is represented by the purple point.
Drag the Point tool to the purple point Drag the Point tool to the purple point to see the coordinates.
Drag the Point tool back to its place. Drag the Point tool back to its place.
Demonstrate moving line.

Point the red cross mark in the formula box.

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).

Drag the blue point to (5,5). Then drag the blue point to (5,5).
Point to y-axis and slope. Notice that line is parallel to y-axis and slope is undefined.
Click on Save line. Click on Save line. Line is saved.
Drag the purple point along the x-axis.

Point to Slope .

Drag the purple point along the x-axis.

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

move the cursor to Game screen. Now let us move on to Game screen.
Go to Line Game tab

Point to the levels.

Click on Line Game screen.

Line Game screen has 6 difficulty levels, to play.

These games will test the knowledge gained using this simulation.

Point to Timer and Sound buttons It has a Timer and Sound buttons at the bottom of the screen.
Click on each game >> explore. Click on each game and explore.
Slide Number 9

Summary

Lets summarize.

In this tutorial, we have learnt,

About Graphing Lines, an interactive PhET simulation.

Slide Number 10

Summary

Using this simulation, we have learnt,

About Cartesian coordinate system with x and y axes.

How to calculate the slope of a graphed line.

To save the plotted lines

How to change the slope and intercept of the line

How changing variables in a linear equation will affect the line.

Slide Number 11 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.

Slide Number 12

About the Spoken Tutorial Project

The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.

Slide Number 13

Spoken Tutorial workshops

The Spoken Tutorial Project team:

conducts workshops using spoken tutorials and

gives certificates on passing online tests.

For more details, please write to us.

Slide Number 14

Forum for specific questions:

Do you have questions in THIS Spoken Tutorial?

Please visit this site

Choose the minute and second where you have the question

Explain your question briefly

Someone from our team will answer them

Please post your timed queries in this forum.
Slide Number 15

Acknowledgement

This project is partially funded by Pandit Madan Malaviya National Mission on Teachers and Teaching.
Slide Number 16

Acknowledgement

Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

This tutorial is contributed by Spoken tutorial team IIT Bombay.

Thank you for joining.

Contributors and Content Editors

Madhurig

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