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# Equations for Parallel and Perpendicular Lines.

Lesson 10 of 20

## Objective: SWBAT write the equation of parallel and perpendicular lines based on the given information.

## Big Idea: For students to write the equation of a line parallel to or perpendicular to a line and passing through a given point using different representations of linear functions.

*55 minutes*

#### Warm up

*10 min*

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.

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#### Power Point

*15 min*

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:

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#### Independent Practice

*20 min*

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.

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#### Exit Slip

*10 min*

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.

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Introduction to Sequences
- LESSON 2: The Recursive Process with Arithmetic Sequences
- LESSON 3: Recursive vs. Explicit
- LESSON 4: Increasing, Decreasing, or Constant?
- LESSON 5: Change Us and See What Happens!
- LESSON 6: Why are lines parallel?
- LESSON 7: Get Perpendicular with Geoboards!
- LESSON 8: Dueling Methods for Writing the Equation of a Line
- LESSON 9: Comparing Linear Combinations in Ax +By= C to y=mx +b
- LESSON 10: Equations for Parallel and Perpendicular Lines.
- LESSON 11: Assessment of Graphing Lines through Art!
- LESSON 12: Are x and y Directly or Inversely Proportional? (Day 1 of 2)
- LESSON 13: Are x and y Directly or Inversely Proportional? (Day 2 of 2)
- LESSON 14: Writing, Graphing, and Describing Piecewise Linear Functions
- LESSON 15: Introduction to Scatter Plots, Line of Best Fit, and the Prediction Equation
- LESSON 16: Predicting the Height of a Criminal (Day 1 of 2)
- LESSON 17: Predicting the Height of a Criminal (Day 2 of 2)
- LESSON 18: Predicting Bridge Strength via Data Analysis (Day 1 of 2)
- LESSON 19: Predicting Bridge Strength via Data Analysis (Day 2 of 2)
- LESSON 20: Linear Assessment