Graphing Parallel and Perpendicular Lines (Day 2 of 2)

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SWBAT write the equation of lines that are parallel and perpendicular.

Big Idea

Students will connect the main ideas from the previous four lessons to write the equations of parallel and perpendicular lines using given information.


10 minutes

Students will complete the Do Now in 5 minutes. 

The aim of this Do-Now is to remind students of how the presence of a negative sign changes an equation. The Do-Now and today's lesson both allow students to practice MP6, as students will be solving equations and must pay special attention to accuracy.

We will review the answers to the Do-Now aloud. I will ask students to score their own paper.

Next, a student will read the objective: "SWBAT write the equation of lines that are parallel and perpendicular."

Guided Notes + Practice

40 minutes

We will open up class using this graphic organizer.

As a review from our last class, I will ask students to write the equations of the four colored lines on the top of their paper. Then, I will ask students to underline the slope of each line. 

  • Underneath the first graph students will write: Parallel lines have the same slope.
  • Underneath the second graph students will write: Perpendicular lines have opposite reciprocal slopes.

Students will then practice finding the opposite reciprocal of a number.

Next, we will complete the first example. I will call on a student volunteer to read the prompt to the class. I found it helpful for students to create a list underneath of the example problem to help organize their thoughts and to help them comprehend what each question is asking.

    • Find the equation of a line that is parallel to y = 2x + 5, and that passes through the point (-1, -1). 
      • Line One: y = 2x + 5
      • Line Two: ???? ( We don't know know the equation of line two)


I will use the following prompts to guide students to creating their own equation:

  • "Our goal is to find the equation of a new line, Line Two, that fits specific criteria."
  • "What are the rules that Line Two must follow?" 
  • "Do we know any values for Line Two now?" 
  • "Why does Line Two have to have a slope of 2?" 
  • "Do we know anything else about Line Two?" 
  • "How can we figure out the equation of a line using what we have?" 

Students will then solve for b and create the equation of a the line y = 2x + 1. Students will use the graph on their paper to check their answer.

Lastly, Students will use what they have learned to write the equations of parallel and perpendicular lines by completing this assignment. I will encourage students to check their responses by graphing the equations that they create on a separate piece of graph paper.

Partner Activity

20 minutes

The class will complete the Rectangle Investigation individually or with a partner. In this activity students will be asked to graph several equations using colored pencils.  Students will then analyze the slope of each equation to answer questions relating to the rectangle that is formed by the intersecting lines.

Instructional Note: Students will need colored pencils to complete this activity


10 minutes

Two volunteers will give a short summary about what we learned in class today. I will then ask students to describe how they can use a coordinate plane to check their answers when graphing equations of a line that are parallel and perpendicular. Students will then complete an exit card. The exit cards should be graded directly after class, and the students should then be grouped by the percentage of correct questions for the review during our next class.