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6.6

6.6. Parallel & Perpendicular Lines. 6.6 – Parallel & Perp. Lines. Goals / “I can….” Determine whether lines are parallel Determine whether line are perpendicular. Mini Quiz 45. 1.Find the reciprocal of each fraction a. b. c. d. 2.Find the slope and y-intercept of each equation.

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6.6

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  1. 6.6 Parallel & Perpendicular Lines

  2. 6.6 – Parallel & Perp. Lines • Goals / “I can….” • Determine whether lines are parallel • Determine whether line are perpendicular

  3. Mini Quiz 45 1.Find the reciprocal of each fraction a. b. c. d. 2.Find the slope and y-intercept of each equation

  4. Quick Review/Preview 1. What is the Slope-InterceptForm? y = mx + b 2. What is the Standard Form? Ax + By = C 3. What is the Point-Slope Form? y – y1 = m(x – x1) 4. Find the “negative reciprocal” of each fraction

  5. Various Forms of an Equation of a Line. Slope-Intercept Form Standard Form Point-Slope Form

  6. Write an equation given the slope and y-intercept EXAMPLE 1 Write an equation of the line shown.

  7. 7 7 3 3. m = – , b = 2 2 4 3 y =– x + 4 y =x + 1 3 for Example 1 GUIDED PRACTICE Write an equation of the line that has the given slope and y-intercept. 1. m = 3, b = 1 ANSWER ANSWER 2. m = –2 , b = –4 ANSWER y = –2x – 4

  8. 6.6 – Parallel & Perp. Lines • Parallel lines are two lines that NEVER intersect. • Two lines are parallel if they have the SAME slope and different y-intercept.

  9. Parallel lines Lines in the same plane that do not intersect are called parallel lines. Parallel lines have the same slope.

  10. 6.6 – Parallel & Perp. Lines • Example: • Are these two lines parallel? y = -2x – 1 4x + 2y = 6 • Since they are in different forms, you need to switch them to the same form. y = -2x – 12y = -4x + 6 2 2 2 y = -2x + 3

  11. Parallel Lines Determine if the lines are parallel 1. 2x + 6y = 12 6y = -2x + 12 yes

  12. Parallel Lines Determine if the lines are parallel 2. 6x + 8y = -24 8y = -6x – 24 No

  13. 6.6 – Parallel & Perp. Lines • Given a line and another point, can you write a parallel line?

  14. Equations of Parallel Lines 4. Write an equation for the line that contains (5, 1) and is parallel to m =

  15. Equations of Parallel Lines 5. Write an equation for the line that contains (2, -6) and is parallel to m = 3 y + 6 = 3(x – 2)

  16. 6.6 – Parallel & Perp. Lines • Perpendicular lines are lines that intersect to form a right angle. • Two lines are perpendicular if the product of their slopes is – 1. This means that the slopes are opposite reciprocals.

  17. Perpendicular Lines Lines that intersect at right angles are called perpendicular lines. The slopes of these lines are opposite reciprocals. Opposite reciprocals???? 3…..

  18. Perpendicular Lines What is the slope of the perpendicular line? 7. -5/2 8. 5/1 = 5 9. 1/2

  19. Equations of Perpendicular Lines 10. Find the equation of the line that contains (0, -2) and is perpendicular to y = 5x + 3 m =

  20. Equations of Perpendicular Lines 11. Find the equation of the line that contains (1, 8) and is perpendicular to m =

  21. Equations of Perpendicular Lines 12. Find the equation of the line that contains (2, -3) and is perpendicular to m = 2 y + 3 = 2(x – 2)

  22. Perpendicular Lines 13. Determine if the lines are perpendicular: and No 14. Determine if the lines are perpendicular: and Yes

  23. Challenge • What is the slope of the line that is parallel to x = 4? undefined • What is the slope of the line that is perpendicular to x = 4? zero

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