# Slopes of Parallel and Perpendicular Lines Objective: To discover the relationships between the slopes of parallel lines and perpendicular lines

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<ul><li><p>Slopes of Parallel and Perpendicular LinesObjective: To discover the relationships between the slopes of parallel lines and perpendicular lines.</p></li><li><p>What type of lines do lines p and q look like?</p></li><li><p>Answerp and q appear to be parallel lines!</p><p>How can we use mathematics to be sure they are indeed parallel?</p></li><li><p> Calculate the slope of each.</p></li><li><p>slope of p = slope of q = = </p></li><li><p>What do you notice about the slopes of these two lines?The slopes are congruent.parallelcongruent</p></li><li><p>Parallel Conjucture:Two lines are parallel if their slopes are equal.Recall the definition of parallel lines then write a few sentences describing why it makes sense that parallel lines would have equal slopes.</p></li><li><p>Are these lines parallel?slope a = -slope b = -NO The slopes are not </p></li><li><p>Are these lines parallel?slope c = slope d = =YES Slopes are </p></li><li><p>You will be shown the slopes of two lines. Write down whether each pair of lines are parallel or not.</p></li><li><p>slope of line r =</p><p>slope of line s = </p><p>These lines are parallel.</p></li><li><p>3. slope of line t =</p><p>slope of line u = </p><p>These lines are parallel.</p></li><li><p>4. slope of line t =</p><p>slope of line u = </p><p>Not parallel because the slopes are not congruent to each other.</p></li><li><p>Ex. Determine whether the graphs of y = -3x + 4 and 6x + 2y = -10 are parallel lines.Step 1: make both equations in the y-intercept form to compare slopes6x + 2y = -10 can be changed to y-intercept form by solving for y</p></li><li><p> 6x + 2y = -10-6x -6x 2y = -6x -10 2 2 2y = -3x - 5Subtract 6xDivide by 2</p></li><li><p>Step 2: compare the slopes of both equations.The first equation y = -3x + 4 has a slope of -3 and the second equation has the same slope of -3Therefore, the graph of the lines will be parallel.</p></li><li><p>Practice: Determine whether the graphs are parallel lines (without graphing) 3x - y = -5 and 5y -15x = 10 4y = -12x + 16 and y = 3x + 4</p></li></ul>

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