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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 + 12 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 + 12 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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