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Bell Ringer

Bell Ringer. What is the slope of the following equations? a. y = x + 9 b. y = -2x – 8 c. y = 7 + 4x d. y = 5 – x. The slope is the coefficient of x. That means the number in front of x. 1 2. 1 2. -2. 4. 2 3. -2 3. Homework. -5 & 10 6 & -8.5 16 & -8 -5.3 & 4

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Bell Ringer

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  1. Bell Ringer • What is the slope of the following equations? a. y = x + 9 b. y = -2x – 8 c. y = 7 + 4x d. y = 5 – x The slope is the coefficient of x. That means the number in front of x. 1 2 1 2 -2 4 2 3 -2 3

  2. Homework • -5 & 10 • 6 & -8.5 • 16 & -8 • -5.3 & 4 • 11 & -11 • 9 & -19 • -6 & 6 • 12 • -12 • 11 • 3 • 11 • 16 • 3 & -7 • 7 & -2.3

  3. News… • All late work due tomorrow for 3rd quarter report cards. • We will begin a new unit today! Yeah! • No school Friday! Yeah! • Report card pick up – April 19th • PSAE April 24th & 25th Only 11th graders will be in school! That means no school for you! YEAH!

  4. GRE 604: Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point PPF 301: Exhibit some knowledge of the angles associated with parallel lines PPF 401: Find the measure of an angle using properties of parallel lines PPF 402: Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°) PPF 501: Use several angle properties to find an unknown angle Parallel and Perpendicular Lines

  5. Parallel Lines • Lines in the same plane that do not intersect are called parallel lines. • Parallel lines have the same slope. These two lines are parallel. They will never intersect!

  6. Parallel Lines • You can also identify parallel lines by their equations! y = 3x + 7 y = 3x – 9 These two lines are parallel. Their slopes are the same! (Notice that they have different y-intercepts!)

  7. Parallel Lines • Which of the following equations are parallel? A. y = 5x + 7 B. y = 2x – 8 C. y = -2x + 1 D. y = 2x – 9 E. y = 5 + 4x F. y = -9 + 6x G. y = 6x – 7 H. y = 8 – 2x I. y = 5x – 1 J. y = -3x + 1 K. y = 7 + 4x L. y = -3x

  8. Perpendicular Lines • Lines that intersect at right angles (900) are perpendicular. • Perpendicular lines have slopes that are negative reciprocals. • The product of their slopes = -1. These two lines are perpendicular. They intersect at a right angle.

  9. Perpendicular Lines Negative reciprocals 1. What is the reciprocal of ? 2. What is the reciprocal of 3? 2 3 3 2 So the negative reciprocal is – ! 3 2 1 3 So the negative reciprocal is – ! 1 3

  10. Perpendicular Lines These equations are perpendicular: y = 2x + 8 y = - x – 5 y = - x – 7 y = x + 5 2 • - ½ = -1 The products of their slope equal -1! 1 2 3 2 4 5 - 4/5 • 5/4 = -1 The products of their slope equal -1! 5 4

  11. Perpendicular Lines • Are these equations perpendicular? A. y = 4x + 7 B. y = - x – 8 y = - x + 9 y = x – 5 C. y = 3x – 2 D. y = 2 + 5x y = x – 8 y = - x + 3 E. y = 8x – 7 F. y = 8 – 2x y = 7 + x y = 2 + x 2 3 Yes! Yes! 1 4 3 2 Yes! No! 1 3 1 2 No! Yes! 1 8 1 2

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