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Lines and Slopes: Parallel & Perpendicular Concepts

Explore the concepts of parallel and perpendicular lines, average rate of change, and slope relationships through guided practice examples. Learn how to determine equations of lines parallel or perpendicular to given lines and calculate average rate of change.

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Lines and Slopes: Parallel & Perpendicular Concepts

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  1. A3 2.4 Parallel and Perpendicular Lines, Avg. rate of change Homework: p. 267-268 1-29 odd

  2. Slope and Parallel LInes • If 2 non-vertical lines are parallel, they have the same slope. • If 2 distinct non-vertical lines have the same slope, then they are parallel. • Two distinct vertical lines, both with undefined slopes, are parallel. Guided Practice: Write an equation of the line passing through (-3,1) that is parallel to y = 2x + 1.

  3. Slope and perpendicular lines • If two non-vertical lines are perpendicular, then the product of their slopes is a – 1. (the 2 slopes are negative reciprocals of each other) • If the product of the slopes of 2 lines is a -1, then the 2 lines are perpendicular. • A horizontal line having a slope of zero is perpendicular to a vertical line having undefined slope. Guided Practice: Write the equation of the line passing through (3,-5) and perpendicular to x + 4y – 8 = 0. Express your answer in general form.

  4. Average Rate of change If the graph of a function is not a straight line, the average rate of change between 2 points is the slope of the line containing the 2 points. The line is called a secant line. Average Rate of Change: Example:

  5. Whiteboard Practice • Write an equation in slope-intercept form for the line parallel to y = - 5x + 4 and passing thru (-2, -7). • Write an equation in slope-intercept form for the line perpendicular to x + 7y – 12 = 0 and passing through (5, -9) • The graph of f passes through (-5, 6) and is perpendicular to the line that has an x-intercept of 3 and a y-intercept of -9. Write an equation in slope intercept form.

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