GeoGebra to find Rate of Change

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GeoGebra is a free software available online at geogebra.org. This program is specifically designed for making graphs. If you do not have MS Office, or would prefer a more direct approach to graphing, GeoGebra is a good choice for you.

When you go to GeoGebra's website, select the green 'Software' button on the left side. You will be taken to a new page where you will have the option of downloading GeoGebra in several formats. Please select a format from the 'GeoGebra Desktop' list.

If you are using Google's Chrome browser, the Chrome app is the easiest way to install GeoGebra. If you are not using Chrome (ie. Explorer, Safari, or FireFox), you will need to install GeoGebra using another format. Select your operating system (Windows, Mac, Ubuntu, etc) from the list to install GeoGebra to your computer.

* You can also download GeoGebra to an Android or Apple device, but for this lesson, we will need to use GeoGebra from a computer.

Once you've downloaded GeoGebra, open the program. If you used Chrome, you'll find GeoGebra in the Apps list. You can access Chrome's Apps list by selecting the little color squares in the top left of your Chrome browser. If you downloaded GeoGebra in another format, please locate the file and open where GeoGebra saved. It may have installed an icon on your Desktop, so check there first.

Below is what the Chrome App list looks like if you used Chrome.

Once GeoGebra has opened, look to the bottom of the screen. You will see an 'Input' field along the bottom. This input field will allow us to enter our coordinates. Click inside the input field, and type your coordinates in one at a time. Input the coordinates with parenthesis and a comma.

After you've entered the coordinates, (3, 25) and (5, 85), points will be added on your graph, though you may not see them appear.

By default, GeoGebra's window does not extend far enough to show points. To correct this, we're going to adjust the window. To adjust the window, right click in the white of your graph. From the drop down menu that appears, select 'xAxis : yAxis', and from the new drop down menu, select the circle by '1 : 20'.

This will adjust your window to count by 20 along the yAxis. By counting by 20, your two points should now appear.

Now that our points are visible on our graph, create a line between these points using the 'Line' tool in the upper left. Once you've clicked on the line tool, move your cursor over one of your two points. As you get close to the point, GeoGebra will jump to the point; once it has snapped to the point, left click. This will create the first point of your line. As you move the cursor now, you should see a line following your cursor. Move the cursor to the second point, and left click on it. This will create a straight line through your two points.

Once you've clicked on the second point, the line should be created through the two points, and an equation should appear in the left side of your window. This is the equation of our line. By default, this equation is written General Form (ax + by = c).

We want to format this equation to be written in Slope-Intercept form (y = mx + b).
To change our equation's format, right click on the the equation. From the drop down menu, click 'Equation y = mx + b'. This should change your equation to be written in Slope-Intercept form.

Now that our line's equation is written in Slope-Intercept, we can use the slope (m's value) to determine our rate of change. The value of m is the rate of change.

Remember that m is always pair with the x variable.