Learning Exercise

Point-Slope Form

Students are given the task of deriving a linear equation by knowing only two points on a coordinate system.
Course: Algebra I

Website for the Science & Mathematics Education Center of Fresno State University see more


When students walked into the classroom the lesson warm-ups were ready on the overhead. The warm-ups were important because they reviewed the pre-requisites needed for this lesson. An example of a warm-up question would be; What is the slope and y-intercept of the equation y = 3x + 4? During the warm-ups we discussed the meanings of particular vocabulary words like: Slope, point or ordered pair, y-intercept, linear equation, function, coordinate system, deriving. This was done as a general review and to ensure everyone was on the same page. After warm-ups, I asked the class a challenging question. "How would I derive an equation from just two ordered pairs?" After some discussion they were still clueless, so I then asked them what things are needed in order to give an equation of a line. We made a list on the white board and came up with: Slope, y-intercept, x-intercept. From that point, some students saw that they could figure out the slope of the points using the slope formula, but got stuck after that. Other students figured out the slope and tried to extend the line betweent the two points to figure out where it crossed the y-axis. The only problem with that is that I purposely made the line cross on a decimal point of the y-axis. Then one student looked in his text book and seen something called the point-slope formula. So we discovered what was needed in order to use the point-slope formula, and how to use it. Once the students had a pretty good understanding of what the point-slope formula was, we began to do some examples. The first example asked for a equation of a line with a specific slope and a specific y-intercept. The second example asked for the equation of a line containing a certain point and a specific slope. The last example asked for the equation of a line containing two specific points. The first two examples were done together on the white board. The last example had six similar problems, so I divided the class into six groups of 3 or 4 students and assigned each group a different problem. There task was to come up with a linear equation and show the rest of the class how they got it. Their presentations were to be done on the white board. My Goal of their presentations was not to see what answer they got but it was to see how they got their particular answer and the reasoning behind it. The students that got the wrong answer quickly saw what they did wrong as they tried to explain it.


Technical Notes

The lesson was delivered on the overhead, and the students used white boards to show how they got their answers. Pencil and paper was used for students to take notes on their classmates' presentations.


The students must have a clear understanding of the following vocabulary words and concepts: Slope, point, y-intercept, linear equation, function, coordinate system.


The topics in this lesson included the following: Point-slope formula, y-intercept and x-intercept, ordered pairs on a graph, deriving a linear equation.

Learning Objectives

For students to become effecient in deriving a linear equation by using the point-slope formula.


After the lesson and the presentations were completed. A five question quiz was given as an assessment. I was looking for two specific things: Their overall understanding of point-slope formula (what is needed in order to use this formula), and a good understanding of the concept (one challenging question was asked in the quiz).