## Brief Activity on Graphing Lines

This week my elementary algebra classes are in the middle of learning to graph lines. I make a big deal about finding the most efficient way to graph a particular line:

• Should you graph this line by using its slope or its intercepts?
• Is this line horizontal or vertical?

I emphasize this in class because it helps students to develop the critical thinking that they need in order to be successful in an introductory statistics class.

This Wednesday I walked into class and asked each student to take out a sheet of paper. I wrote the following prompt on the board.

Write the equation of a line that …
1) is horizontal.
2) you would graph using its x- and y-intercepts,
3) is vertical.
4) that you would graph using its slope and y-intercept.

I gave them 3 minutes to write their answers for the 4 questions. Many of my students did well, but there were a few that struggled with a couple of answers and a few more students that didn’t know where to begin. I then put the students together with their groups of 4 and asked them to assemble one common set of equations. This gave those students who were struggling to hear the insight of their classmates. I think it was really effective, and noticed that the graphing went much smoother today when we were discussing parallel and perpendicular lines.

Students who struggle on this exam often struggle because they can’t figure out how to get started, and I think this is because they haven’t really thought about how to choose an efficient technique for graphing a particular line. I’ll let you know how it goes.

Do you have experience with activities to help students become efficient graphers? Are you a student who is unsure how to choose the most efficient technique to graph a line quickly and accurately? Please leave a comment, or reach me through the contact page at my web site – georgewoodbury.com.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

• 1. Dave Radcliffe  |  February 17, 2011 at 2:43 pm

y = 0; x/2 + y/3 = 1; x = 0; y = 2x.

I find that students are often confused when they are asked a question that has many correct answers, or requires an arbitrary choice. Maybe we don’t ask these kinds of questions often enough.

• 2. georgewoodbury  |  February 18, 2011 at 8:11 am

I agree – I could tell that many of the students were not used to being asked a question like this and it took them a moment to get going.

• 3. j edward ladenburger  |  February 17, 2011 at 9:42 pm

I usually stress efficient linear graphing methods in a backdoor fashion, by emphasizing the information provided “by inspection” for various forms of linear equations in two dimensions.

For example, $$\frac{x}{a} + \frac{y}{b} =1$$ is called the two-intercept form because $$a$$ and $$b$$ are the x and y intercepts respectively.

$$y – y_1 = m ( x – x_1)$$ is called the pint-slope form because you can read the slope $$m$$ and a point $$( x_1, y_1 )$$ directly from the equation.

By focusing on the various forms and their names, and by allowing students the freedom to choose an appropriate form from the very first introduction of linear equations, they seem to naturally become efficient graphers.

• 4. j edward ladenburger  |  February 17, 2011 at 9:45 pm

Sorry — I see that the LaTeX coding did not work… hope the comment is still comprehensible

x/a + y/b = 1

and

y – y1 = m ( x – x1 )