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Mastering Parallel and Perpendicular Lines: Equations and Concepts

Learn to define and find equations for parallel and perpendicular lines, including identifying slopes, y-intercepts, and writing equations. Practice with exercises to solidify understanding.

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Mastering Parallel and Perpendicular Lines: Equations and Concepts

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  1. Parallel and Perpendicular Lines Objectives: Define parallel lines. Find equations of parallel lines. Define perpendicular lines Find equations of perpendicular lines.

  2. Parallel Lines • Slopes of parallel lines are equal. • Recall the steps of finding an equation of a line. • Find slope • Find the y-intercept • Write the equation • This is the same process when working with parallel and perpendicular lines.

  3. Find an equation of a line passing through (-2,5) that is parallel to 3x + 2y = 9 • Find slope: • Get y by itself in the given equation 2y = 9 – 3x y = 9/2 – 3/2 x slope=-3/2 • Find y-intercept: • Use a slope of -3/2 since the lines are parallel y = -3/2 x + b 5 = -3/2 (-2) + b 5 = 3 + b 2 = b • Write equation: y = -3/2 x + 2

  4. Perpendicular Lines • Perpendicular lines have negative reciprocal slopes. • If a line has a slope of -1/2 the perpendicular line would have a slope of 2. • If a line has a slope of 5/6 the perpendicular line would have a slope of -6/5 • What would be the slope of a line perpendicular to a line with a slope of -7? 1/7

  5. Find the equation of the line passing through (-1,3) that is perpendicular to 3x – 2y = 8. • Find slope • Get y by itself: -2y = 8 – 3x y = -4 + 3/2 x • Slope is 3/2 so perpendicular slope is -2/3 • Find y-intercept • y = -2/3 x + b 3 = (-2/3)(-1) + b 3 = 2/3 + b 3 – 2/3 = b 7/3 = b • Write equation y = -2/3 x + 7/3

  6. Review concepts learned • Parallel lines have equal slope • Perpendicular lines have negative reciprocal slopes. • To find an equation of a line • Find slope • Find y-intercept • Write equation

  7. Assignment • Page 197 • #7, 11, 13, 17, 21, 23, 25, 29, 33, 37

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