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4.6 Slope Objectives: Understand the concept of slope

4.6 Slope Objectives: Understand the concept of slope Know the slope of parallel and perpendicular lines. Slope: steepness and direction. positive slope. negative slope. m = 1 . m = 2 . no slope. m = ½ . m = 0. m = –2 . m = –1 . no slope. m = – ½ . m = 0.

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4.6 Slope Objectives: Understand the concept of slope

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  1. 4.6 Slope Objectives: • Understand the concept of slope • Know the slope of parallel and perpendicular lines

  2. Slope: steepness and direction positive slope negative slope

  3. m = 1 m = 2 no slope m = ½ m = 0

  4. m = –2 m = –1 no slope m = –½ m = 0

  5. The symbol Δ is read “delta” and is used to indicate change. Example 1: Find the slope of these lines: a) A(–4,0) and B(–5,7)

  6. What is the slope of parallel lines?

  7. Theorem 26: If two non-vertical lines are parallel, then they have the same slope. Theorem 27: If the slopes of two non-vertical lines are equal, then the lines are parallel.

  8. Example 2: Are these lines parallel? y = 3x – 6 y= 3x + 4

  9. Theorem 28: If two lines are perpendicular and neither is vertical, then each line’s slope is the opposite reciprocal of the other’s. Theorem 29: If a line’s slope is the opposite reciprocal of another line’s slope, then they are perpendicular.

  10. Example 3: Are these lines parallel, perpendicular, or neither? m1 = –2 m2 = –2 m3 = ½ m4 = 2 m5 = 0 m6 = undefined ℓ1- (4, 5) & (3, 7) ℓ2- (3, 6) & (8, –4) ℓ3- (4, 3) & (6, 4) ℓ4- (–1, 0) & (2, 6) ℓ5- (–3, 4) & (2, 4) ℓ6- (–2, 0) & (–2, 7)

  11. Example 4: a) Prove ΔCEF is a right triangle. C(1, 3), E(8, 4), F(4, 7) b) Find the slope of the median to . c) Find the slope of the altitude to .

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