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SLOPE

SLOPE. Objective: to find the slope of a line. When we talk about slope, we are referring to the steepness of a line. When lines are going up from left to right, we say they have a positive slope. When lines are going down from left to right, they have a negative slope.

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SLOPE

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  1. SLOPE Objective: to find the slope of a line

  2. When we talk about slope, we are referring to the steepness of a line. When lines are going up from left to right, we say they have a positive slope.

  3. When lines are going down from left to right, they have a negative slope

  4. When lines are horizontal, their slopes are zero

  5. When lines are vertical, their slopes are undefined

  6. Think about snow skiing… • Positive slope- going up a mountain • Negative slope- going down a mountain • Zero slope-cross country skiing, no incline • Undefined slope- impossible!!!!

  7. Rally Robin Determine whether each slope will be positive, negative, zero, or undefined

  8. Both slopes are negative, because they are going downhill. Notice how the first skateboarder is going down a steeper ramp.  The slope of that line is bigger than the slope of the second skater's line.

  9. The steeper the line, the higher the slope

  10. Now…. How to find the exact value of the slope Rise/Run

  11. Or… slope formula (blue sheet) It is not known why the letter m was chosen for slope; the choice may have been arbitrary. John Conway has suggested m could stand for "modulus of slope." One high school algebra textbook says the reason for m is unknown, but remarks that it is interesting that the French word for 'to climb' is monter. However, there is no evidence to make any such connection. Descartes, who was French, did not use m. In Mathematical Circles Revisited (1971) mathematics historian Howard W. Eves suggests 'it just happened.

  12. Slope Formula

  13. Examples:

  14. Sage n Scribe slope

  15. Slopes of parallel and perpendicular lines • Parallel lines have the same slope • Ex. 2/3 and 2/3 or -5 and -5 • Perpendicular lines have slopes that are opposite reciprocals of each other • Ex. 2/3 and -3/2 or -5 and 1/5

  16. Now let’s try some practice in your textbook • P. 142 (15-37) odd for practice

  17. Homework • Page 142(16-38) even

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