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Understanding Slopes: Key Concepts and Applications in Lines

This lesson focuses on the fundamental concepts of line slopes, including the calculation and interpretation of slopes. Students will learn that the steepness of a line is determined by the absolute value of its slope, with larger values indicating steeper lines. The lesson covers positive slopes (uphill), negative slopes (downhill), horizontal (zero) slopes, and vertical (undefined) slopes. Additionally, it discusses the properties of parallel and perpendicular lines, highlighting the significance of their slopes. Guided practice exercises will reinforce these concepts.

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Understanding Slopes: Key Concepts and Applications in Lines

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  1. Lesson 3.4 Find and Use Slopes of Lines

  2. Key Concept • y2 – y1 x2 – x1 • Steepness of a line is determine by the absolute value of the slopes. Therefore +/- slopes don’t factor into the steepness of a line!!!! • Bigger the absolute value the steeper the line • y = -4x + 2 is steeper than y = 3x - 3 • Negative Slope- “downhill” Left to Right • Positive Slope- “Uphill” Left to Right • Horizontal Slope- Slope is zero: 0/# • Vertical Slope- Slope is Undefined: #/0 m =

  3. Postulate 17 • Slopes are the same with parallel lines because they never intersect

  4. Postulate 18 • All perpendicular lines have negative(opposite) reciprocal (flip) slopes; such that the product of their slopes equal -1. • Ex: y = 2x + 3 & y= -1/2x – 2 m=2 m= -1/2 m=2/1 m = ½ -1/2 • 2(-1/2)= -1 ; Therefore the product of the slopes is -1 “Flip” “Opposite”

  5. Guided Practice • Pg. 171-173; #’s 1-7all

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