Welcome to this tutorial on Graphing Lines simulation.
In this tutorial, we will demonstrate Graphing Lines, an interactive PhET simulation.
To follow this tutorial, learner should be familiar with topics in high school mathematics.
Here I am using: Ubuntu Linux OS version 14.04 Java version 1.7 Firefox Web Browser version 53.02.2
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
4. How to change the slope and intercept of the line 5. How changing variables in a linear equation will affect the line.
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.
Use the given link to download the simulation.
I have already downloaded Graphing Lines simulation to my Downloads folder.
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.
This is the interface of Graphing Lines simulation.
The interface has four screens-Slope, Slope-Intercept, Point-Slope and Line Game.
Click on Slope screen.
Screen has a Cartesian coordinate system with x and y axes.
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, and x2, x1 are 3 and 1.
A graph is plotted using the default values. Here we can see Slope is 1.
We can change the values of y2, y1 and x2, x1 using up and down arrow buttons.
Plotted line can be saved using Save Line button.
We can hide the formula box by clicking on red minus sign. To show the box, click on green plus button.
Below the formula box, we have Slope, Hide lines and Hide grid check boxes.
If we click on Hide lines and Hide grid check-boxes, graph and grid are hidden. Automatically Slope check-box is disabled.
Let's uncheck Hide lines and Hide grid check boxes to enable Slope check box.
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.
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 Point tools on purple and yellow points to see the coordinates.
Drag the Point tools to the bottom.
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 to coincide with (5,5). Observe that slope of the line is 1.
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. This confirms that yellow point is at(2,8).
Now Slope is 4.
Click on Save Line in the formula box. Line is saved.
Drag the yellow point to (-5,5). Drag and place Point tool on yellow point.
Now Slope is -1.
Click on Save Line in the formula box. Line is saved.
Drag the point tool back to place. Drag the yellow point to (-2,8).
Here Slope is -4.
Click on Save Line. Line is saved.
We have drawn 4 lines with different slopes. Notice that steepness is related to slope.
As an assignment: 1. Find when slope is zero and when it is undefined. 2. Give an explanation.
Now, let us explore Slope-Intercept screen at the bottom of the interface.
Click on Slope-Intercept screen. Screen opens with a line y= 2/3x+1 (2 by 3 x plus 1).
Here intercept value is 1.
In this screen, we can change the values of 'm' and 'b'.
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.
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 to reset the simulation. Click on Save Line. Line is saved.
Change the numerator value of m from 2 to 3 in the formula box. Notice that slope is 1 while Intercept still remains 1.
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. Line is saved.
Change b value to -2, click on Save Line. Line is saved.
We have 3 parallel lines intercepting y-axis at 3 different points.
Click on Reset button to reset the simulation.
Let us change b value to zero. Notice that purple point is at the origin.
Line now passes through the origin.
Click on y=x and y=-x check boxes below the slope. Notice that we have three lines passing through the origin.
Now, let us now move on to Point-Slope screen.
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. In this method, x and y values are defined.
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.
Drag the Point tool to the purple point, to see its coordinates.
Drag the Point tool back to its place.
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).
Then drag the blue point to (5,5).
Notice that line is parallel to y-axis and slope is undefined.
Click on Save line. Line is saved.
Drag the purple point along the x-axis. Notice that Slope is undefined all along the x-axis.
Now, let us move on to Line Game screen.
Click on Line Game screen.
Line Game screen has 6 difficulty levels to play. These games will test the knowledge gained using this simulation.
It has a Timer and Sound buttons at the bottom of the screen.
Click on each game and explore.
Lets summarize.
In this tutorial, we have learnt about Graphing Lines, an interactive PhET simulation.
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
4. How to change the slope and intercept of the line
5. How changing variables in a linear equation will affect the line.
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.
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