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Lesson 5.5 Parallel and Perpendicular Lines 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. Lesson Objective: Students will be able to write equations of parallel and perpendicular lines as demonstrated by a Ticket out the Door. Graph the following on the coordinate plane. y 1 1 y x3 y x 1 2 2 1 m 2 b 3 x 1 m 2 b 1 Parallel lines have the same slope. Parallel lines Two lines are parallel if they never intersect. Example: Parallel lines Not parallel lines Think Pair What do we know Share: about the slope of parallel lines? Graph the following on the coordinate plane. 2 3 y x 1 y x4 y 3 2 2 3 m m 3 2 b 1 x b4 Lines appear perpendicular Perpendicular lines have slopes that are opposite reciprocals Perpendicular Lines Two lines are perpendicular if they intersect to form right angles. Example: Perpendicular Not perpendicular Think Pair What do we know about the of perpendicular lines? Share: Linesslope are perpendicular if the product of the slopes is -1 (opposite and reciprocal). I Do! Find the slope only of a line parallel and perpendicular to the graph of each equation. Example 2: Example 1: m=2 2 y x 1 3 We Do! Find the slope of a line parallel and perpendicular to the graph of each equation. y 3 4( x 2) We Do! Find the slope of a line parallel and perpendicular to the graph of each equation. Think Pair Share: 3x 4 y 12 You Do! Find the slope of a line parallel and perpendicular to the graph of each equation. Partner A on the 2 x y 2 White Board Partner B on the White Board 7x y 5 Determine if the lines in each pair are parallel or perpendicular? 3 y x2 2 3x 2 y 8 Part 1: Parallel Lines Parallel lines: Lines are parallel if they have the same slope but different y-intercepts. Write in slopeintercept form the equation of the line that is parallel to the line in the graph and passes through the given point. Flow map for parallel lines: Step 1: Determine the slope that you will need m= Step 2: take the given point x1 = y1 = Step 3: plug the point and slope into the point - slope formula Step 4: distribute and solve for “y” y = mx + b y – y1 = m(x – x1) Point-Slope Form Stop here if the question asks for Point Slope Form SlopeIntercept Form I Do! Write in slope-intercept form the equation of the line that is parallel to the line y 3x 5 and passes through the point (6, 2). We Do! Write in slope-intercept form the equation of the line that is parallel to the line y 2 x 6 and passes through the point (-4, -6). You Do! Partner A on the Whiteboard: Write in slope-intercept form the equation of the line that is parallel to the line y 6 x 2 and passes through the point (0,1). You Do! Partner B on the Whiteboard: Write in slope-intercept form the equation of the line that is parallel to the line y 2 x 3 and passes through the point (-3,5). Part 2: Perpendicular Lines Perpendicular lines Lines are perpendicular if the product of their slopes equals −1 The slopes are: *opposite *reciprocal Write in slopeintercept form the equation of the line that is perpendicular to the line in the graph and passes through the given point. I Do! Write in slope-intercept form the equation of the line that is perpendicular to the line y 3x 5 and passes through the point (6, 2). We Do! Write in slope-intercept form the equation of the line that is perpendicular to the line y 2 x 7 and passes through the point (0, 1). You Do! Partner A on the Whiteboard Write in slope-intercept form the equation of the line that is perpendicular to the line y x 3 and passes through the point (-1, 2). You Do! Partner B on the Whiteboard Write in slope-intercept form the equation of the line that is 1 perpendicular to the line y 4 x 2 and passes through the point (-1, -2). 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.