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# Why are lines parallel?

Lesson 6 of 20

## Objective: SWBAT change from standard form to slope intercept form, explain the reasoning of why lines are parallel, and write the equation of a line going through a point and parallel to a given line.

## Big Idea: The emphasis in this lesson is that students not only know the definition of parallel lines, but why lines are parallel.

*50 minutes*

#### Warm up

*10 min*

I intend today's Warm up to take about 5 minutes. Students are able to enter both linear equations into the applet and get an instant visual of the 2 lines on the graph. In some cases, students need to solve for y to change the equations from standard form to slope-intercept form. At the end of the warm up, we discuss the fact that knowing the slope of the line is helpful to understanding the relationship between the lines. Also, the idea that when an equation is in slope-intercept form it is easy to identify the slope.

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#### Think, Pair, Share

*30 min*

Students work in pairs for this Activity. My students are already assigned to pairs or threesomes. I assign students homogeneously as much as possible. My room has tables, which makes it easy to implement partner activities. I know that some pairs of students will work at a higher level than others, but I want all students to engage in productive struggle.

For this activity, I give students 5 minutes for individual work, then I allow 5 minutes to work with a partner. At the end of the 10 minutes, I call on pairs (selected during observation) that used different methods to complete the investigation. Most of the students plotted the points well, and made the shape. I demonstrate the shape made in the video below.

I find that sharing with a partner is beneficial for students who have difficulty naming the type of quadrilateral. Students also discussed the relationship between the lines in terms of the slope. I encourage students to use the graph to help verify the sign of the slope. Is it rising from left to right? or Is it falling from left to right?

#### Resources

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#### Exit slip

*10 min*

I assign the Exit slip individually with 10 minutes left in the period to reinforce the objective of the lesson which was to be able to state the relationship between lines and the reasoning to support their answers.

I use this as a formative assessment to check how well students are understanding the relationship between lines and their ability to explain their reasoning.

This problem also allows me to discuss a vertical and a horizontal line on the same graph will always represent perpendicular lines that will always intersect.

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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