Equations for Parallel and Perpendicular Lines.

In this Warm up I intend for the students to reflect on strategies to write the equation of a line parallel to or perpendicular to a given line.  The first two problems are relatively open. Problems 3 and 4 require the parallel or perpendicular line to go through a given point.  I plan for this warm up to take 10 minutes.

An important part of this lesson is using graphs to allow students a visual approach to each problem.  The students are not required to draw the graph in the warm up. Later, I require students to draw the graph for these problems.  Some students will be able to write the equation of the new line without the graph. The Warm Up will provide a good indication of who can and cannot succeed without making a graph.

In this lesson I am building off of the prior knowledge of students knowing the slope of parallel and perpendicular lines and continuing to model multi-step problems with parallel and perpendicular lines. 

I set up the warm up problems in a PowerPoint that I review after the warm up is completed. The PowerPoint contains several additional problems that students will work on for Independent Practice.

I review the  Parallel or Perpendicular problems from the warm up and the problems students are going to work in the independent practice.  I model reviewing the last problem in the power point with the students in the video below:

In this Practice, I give students four different types of problems. The problems are the same four types of problems that were modeled at the end of the PowerPoint.

For the Independent Practice I also provide a graph and ask students to draw a picture of the problem. By having students draw the picture and label line 1 and line 2 in each problem, it helps students to distinguish between the original line and the new one. 

I plan for this Rectangle problem to provide students with an opportunity to apply the concepts and skills from this lesson.  I want students to make explicit use of the their knowledge that opposite sides of a rectangle are parallel, and, consecutive sides of a rectangle are perpendicular. Students first prove that this is true by verifying that  the opposite sides of a rectangle on a graph are parallel because they have the same slope. Then, they show that consecutive sides are perpendicular because they have slopes that are opposite reciprocals of each other.

I expect some students will work concretely and calculate slope by counting the boxes. If so, I will build off concrete strategies to wrap up this lesson.  As much as possible I would like to have students explain strategies that involve calculating slopes. I think that students can learn new concepts and strategies by comparing their existing knowledge to that of their peers.

Instructional Note:

In this problem, the answer is that coordinate C should be at the point (6, -8).  Line segments AB and CB both have a slope of 1, and line segments AB and DC both have a slope of -1.