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Parallel and Perpendicular Lines Lesson 5.5

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Alg 7.0 Derive linear equations by using the point-slope formula. Alg 8.0 Understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Find the equation of a line perpendicular to a given line that passes through a given point.

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Lesson Objective: Students will be able to write equations of parallel and perpendicular lines as demonstrated by a Ticket out the Door.

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Graph the following on the coordinate plane. x y Parallel lines have the same slope.

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Parallel lines Two lines are parallel if they never intersect. Example: Parallel lines Not parallel lines What do we know about the slope of parallel lines? Think Pair Share:

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Graph the following on the coordinate plane. x y Lines appear perpendicular Perpendicular lines have slopes that are opposite reciprocals

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Perpendicular Lines Two lines are perpendicular if they intersect to form right angles. Example: Perpendicular Not perpendicular What do we know about the slope of perpendicular lines? Lines are perpendicular if the product of the slopes is -1 (opposite and reciprocal). Think Pair Share:

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I Do! Find the slope only of a line parallel and perpendicular to the graph of each equation. Example 1: m=2 Example 2:

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We Do! Find the slope of a line parallel and perpendicular to the graph of each equation.

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We Do! Find the slope of a line parallel and perpendicular to the graph of each equation. Think Pair Share:

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You Do! Find the slope of a line parallel and perpendicular to the graph of each equation. Partner A on the White Board Partner B on the White Board

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Determine if the lines in each pair are parallel or perpendicular?

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Part 1: Parallel Lines

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Parallel lines: Lines are parallel if they have the same slope but different y-intercepts.

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Write in slope- intercept form the equation of the line that is parallel to the line in the graph and passes through the given point.

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Step 1: Determine the slope that you will need m = Step 2: take the given point x 1 = y 1 = Step 3: plug the point and slope into the point - slope formula y – y 1 = m(x – x 1 ) Flow map for parallel lines: Point-Slope Form Step 4: distribute and solve for “y” y = mx + b Slope- Intercept Form Stop here if the question asks for Point Slope Form

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Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (6, 2). I Do!

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We Do! Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (-4, -6).

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You Do! Partner A on the Whiteboard: Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (0,1).

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You Do! Partner B on the Whiteboard: Write in slope-intercept form the equation of the line that is parallel to the line and passes through the point (-3,5).

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Part 2: Perpendicular Lines

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Perpendicular lines Lines are perpendicular if the product of their slopes equals −1 The slopes are: *opposite *reciprocal

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Write in slope- intercept form the equation of the line that is perpendicular to the line in the graph and passes through the given point.

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I Do! Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (6, 2).

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We Do! Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (0, 1).

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You Do! Partner A on the Whiteboard Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (-1, 2).

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Write in slope-intercept form the equation of the line that is perpendicular to the line and passes through the point (-1, -2). You Do! Partner B on the Whiteboard

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Summary Parallel Lines: They have the same exact slope (m) and different y-intercepts (b) Perpendicular Lines: Their slopes are opposite (change the sign) and reciprocals (flip)of each other.

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