slope objective: to find the slope of a line. when we talk about slope, we are referring to the...

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SLOPE

SLOPEObjective: to find the slope of a lineWhen 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

When lines are horizontal, their slopes are zero

When lines are vertical, their slopes are undefined

Think about snow skiingPositive slope- going up a mountainNegative slope- going down a mountainZero slope-cross country skiing, no inclineUndefined slope- impossible!!!!

Rally RobinDetermine whether each slope will be positive, negative, zero, or undefinedBoth 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.

The steeper the line, the higher the slope

Now. How to find the exact value of the slopeRise/Run

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.Slope Formula

12Examples:

Sage n Scribe slopeSlopes of parallel and perpendicular linesParallel lines have the same slopeEx. 2/3 and 2/3 or -5 and -5Perpendicular lines have slopes that are opposite reciprocals of each otherEx. 2/3 and -3/2 or -5 and 1/5

Now lets try some practice in your textbookP. 142 (15-37) odd for practiceHomeworkPage 142(16-38) even

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