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Parallel Lines

y. x. Parallel Lines. Two nonvertical lines are parallel if and only if they have the same slope. Parallel lines are two straight lines that never touch. m 1 = m 2. Slope m 1. Parallel lines have the same slope, but different y-intercepts. Slope m 2. Parallel Lines. Slope of Line 1.

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Parallel Lines

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  1. y x Parallel Lines • Two nonvertical lines are parallel if and only if they have the same slope. Parallel lines are two straight lines that never touch. m1 =m2 Slope m1 Parallel lines have the same slope, but different y-intercepts Slope m2

  2. Parallel Lines Slope of Line 1 Slope of Line 2

  3. y x Line d has a slope of Parallel Lines Example: Line c has a slope of If line d is parallel to line c, what is its slope? Parallel lines have the same slope. line c line d

  4. Write the Equation of a line given a Parallel Line and a Point Write an equation of a line that is parallel to the line y = x + 8 and passes through the point (– 6, 4) 1 2

  5. y x Write the Equation of a line given a Parallel Line and a Point Write an equation of a line that is parallel to the line y = x + 8 and passes through the point (– 6, 4) 1 2 Answer: y = x + 7 1 2

  6. Write the Equation of a line given a Parallel Line and a Point Write an equation of a line that is parallel to the line y = x – 2 and passes through the point (– 2, 1) 2 3

  7. Write the Equation of a line given a Parallel Line and a Point Write an equation of a line that is parallel to the line y = – 3 x – 2 and passes through the point (3, – 4)

  8. Write the Equation of a line given a Parallel Line and a Point Write an equation of a line that is parallel to the line y = x + 2 and passes through the point (3, – 2) 1 4

  9. y x Perpendicular Lines Perpendicular lines are two lines that meet in a 90° angle. Perpendicular lines have a slopes that are negative reciprocals of each other. 1 l1 = - m1 m2 OR l2 m1 m2 = -1

  10. Perpendicular Lines Slope of Line 2 Slope of Line 1

  11. Perpendicular Lines • Give the slope of a line perpendicular to the given line. • y = – 4 x +2 • y = x – 3 • y = x – 5 1 2

  12. Write the Equation of a line given a Perpendicular Line and a Point Write an equation of a line that is perpendicular to the line y = – 4x + 6 and passes through the point (0, 2)

  13. Write the Equation of a line given a Perpendicular Line and a Point Write an equation of a line that is Perpendicular to the line y = x + 3 and passes through the point (4, 5) 1 2

  14. Standard Form of a Linear Equation The standard form of a linear equation is Ax + By = C where A and B are not both zero

  15. Forms of Linear Equations • Slope-Intercept Form: Given the slope m and the y-intercept b, use this equation: y = mx + b • Standard Form: • Ax + By = C • where A and B are not both zero

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