Department of Mathematics --- College of Science --- University of Utah

Mathematics 1010 online

To Draw the Line

If you see this red text then unfortunately your browser does not support applets. You may have to enable Java, or use a different system.Click here to see a gif image of the applet that you should be seeing.

The applet just above this paragraph lets you practice drawing straight lines based on various types of information:

One point

Another point .

The slope .

The -intercept .

The -intercept ..

The slope intercept form $\displaystyle y = mx + b$ of a line.

The point slope form $\displaystyle \frac{y-y_1}{x-x_1} = m$ of a line.

The 2-point form $\displaystyle \frac{y-y_1}{x-x_1} = \frac{y_2-y_2}{x_2-x_1}$ of a line

The general form $\displaystyle Ax + By + C = 0$ of a line.

Any one of the last four or any two of the first five items determine the line. You draw the line by setting up a suitable coordinate system and then drawing two points on the line. If your points are correct you are informed, and you can go on to another line, otherwise you get to try again.

Operating the Applet

To make use of the applet proceed as follows:

Click on the applet at the top of this page. A control panel and a drawing window will appear on your screen. If you have the code for the applet you can also activate it from a Unix window by typing java Line
Organize the two windows conveniently on the screen. Resize the drawing window if it's convenient.
Choose two of the first five or one of the last four items in the control window by clicking on the check boxes on the left. The corresponding text windows will light up and give you the relevant information about the line. You cannot pick the second point unless you also pick the first point, and you cannot obtain more information than you need to identify the line. To begin with you may wish to choose just two points, the first two items, to get the hang of operating the drawing window.
Figure out two points on the line (unless you are already given them).
Choose an origin in the drawing window and click on it. Two coordinate axes intersecting at your chosen point will appear.
Click on another point to provide a scale. The maximum horizontal or vertical distance of your second point from your chosen origin will correspond to a distance of . The coordinate axes are labeled and a faint green grid resembling Engineering graph paper is drawn.
Locate one of the points you have determined in the coordinate system and click on it. It will be marked with a small red circle.
Locate your second point in the coordinate system and click on it. If both your points lie on the line (within 10 pixels) the second point and the line are drawn and you have succeeded! If at least one of your points is not on the line the coordinate system is erased and you can start over by choosing an origin. The line in question does not change.
To work with a new line click on the button "New" in the control window.
To give up and list all the information about the current line and draw its graph click on "Show".
To erase your coordinate system, but continue work on the same line, click on "Erase".
When you are done click on "Quit", or click on the applet.

The system generates lines randomly, and it does not keep track of your performance. The purpose of this applet is strictly to help you practice drawing and understanding lines.

The applet on this page may also help you appreciate the following bit of web humor I came across recently:

Euclid's last Theorem. After a while you get to a point where you have to draw the line.