Dueling Methods for Writing the Equation of a Line

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SWBAT write the equation of a line using the slope-intercept form and point-slope form.

Big Idea

The purpose of this lesson is to introduce the students to point-slope form by using a comparison chart with slope-intercept form.

Warm up

10 minutes

Today's Warm up is intended for the students to complete in 5 minutes.  It sets up the introduction of a new model for linear functions. I have not introduced the point-slope form to write the equation of a line previously. Therefore, I instruct my students to complete only the left side of the comparison chart.  In other words, I expect my students to write the equation of a line using slope-intercept form, y=mx + b.

After my students complete the Warm Up, I will demonstrate point-slope form by completing the right side of the comparison chart. I encourage my students to take notes as they follow along and complete the right side of the table with me. I demonstrate introducing the Warm Up and using Point-Slope form in the following video:


Independent Practice

15 minutes

I want to give my students a lot of time for practice today, so I will allow them to work on the Independent Practice until there are about 10 minutes left in the period. The Independent Practice is similar to the Warm-up: students to write the equation of a line using slope-intercept form on one side of the worksheet. On the other side, they use point-slope form.

Because I want students to recognize linear relationships in different forms, in this practice students to write the equations of the lines from different representations:

  • a linear graph
  • a point and a slope
  • two points
  • an x-intercept and a slope
  • two points with the same x value
  • a table

At the end of the Independent Practice I provide a Select All type multiple choice question. Students will be assessed in this format on the PARCC Exam this year.

With about 10 minutes left in the period, I instruct the students to complete the Independent Practice as homework to be handed in the next day and we move on to today's Exit Slip.

Exit Slip

10 minutes

Today's Exit Slip requires about 10 minutes.  It provides me with a quick formative assessment to check student understanding of using Point-Slope Form to write the equation of a line. The students are instructed to use Point-Slope Form, but I expect some students will apply Slope-Intercept Form.

Examples of Student Work

  • Student 1 solved the equation correctly for the y intercept, but then wrote y=3x -17.
  • Student 2 calculated the wrong slope and then distributed incorrectly to the 2nd term in the parentheses. 
  • Student 3 wrote the correct equation y=3x + 17

Based on the examples shown here, I learned that it will be important to emphasize precision (MP6) in future lessons because many errors were small and resulted from a lack of precision in the application of a method.