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**Equations of Parallel and Perpendicular Lines**

Algebra 1 Unit 5: Writing equations of lines

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Parallel Lines

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**What are parallel lines?**

Parallel lines are two lines that never intersect each other.

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**Where have you seen examples in real-life?**

Lines on a road Lines between bricks Floor and ceiling Brainstorm as many examples of parallel lines as possible.

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**What characteristics do parallel lines have?**

Parallel lines are two lines that never intersect each other, BUT: What are their features on a graph? They have the same slope They can have different y- intercepts They still will never intersect

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Parallel Lines

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**Determine if lines are parallel or perpendicular**

1. Put the equation into slope- intercept form ( y = mx +b) 2. Determine if the slopes are the same (parallel) or opposite reciprocals (perpendicular) or neither.

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**Determine if the lines are parallel**

Y = 4x + 16 Y = 3x + 1 Y = -4x – 1 Y = -1/4x – 4 Y = 4x - 2

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**Determine if two lines are parallel**

2x + 4y = 10 9x + 4y = 12 Y = -9/4x – 5 2y = 18/4x + 8 Y = - 3x – 1

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**Writing equations of parallel lines**

I want a line parallel to y = 4x + 10 that goes through the point (6, 12). How would I do this graphically?

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**Writing equations of parallel lines**

I want a line parallel to y = 4x + 10 that goes through the point (6, 12). How would I do this algebraically?

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Example I want a line parallel to y = -2x – 1 and through the point (3, 6).

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Example I want a line parallel to y = 6x and through the point (0, -10).

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Real- Life Example I am creating a city which is to have two parallel streets. If I plot the first street such that the equation is y = 2x – 2 and I want the other street to be 6 units away, what would be the equation of this street?

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Real-Life Example

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Questions?

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Perpendicular Lines

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**What are perpendicular lines?**

Perpendicular lines are two lines that intersect to form a right angle. A right angle is an angle whose measure is 90 degrees.

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**Where have you seen examples in real-life?**

Floor and wall Intersection of two roads Tiles on the ground Brainstorm as many examples of parallel lines as possible.

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**What characteristics do perpendicular lines have?**

Perpendicular lines are two lines that intersect to form a right angle, BUT: What are their features on a graph? They have opposite reciprocal slopes WHY? They can have different y- intercepts

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Perpendicular Lines

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**Determine if two lines are perpendicular**

x - 3y = 10 9x + 4y = 12 Y = -9/4x – 5 2y = 18/4x + 8 Y = - 3x – 1

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**Write equations of perpendicular lines.**

I want a line perpendicular to y = 4x + 10 that goes through the point (6, 12). How would I do this graphically?

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**Write equations of perpendicular lines.**

I want a line perpendicular to y = 4x + 10 that goes through the point (6, 12). How would I do this algebraically?

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Example I want a line perpendicular to y = -2x – 1 and through the point (3, 6).

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Example I want a line parallel to y = 6x and through the point (0, -10).

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Real- Life Example I am designing an intersection. I need the two streets to create a 90 degree angle. If the first street is located on the line y = 4x – 2 where would I need to build the new road to create this intersection such that the road goes through a town located at a point (4, 7)?

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Real- Life Example

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