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SLOPE Objective: to find the slope of a line. When we talk about slope, we are referring to the...

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

SLOPE

Objective: to find the slope of a line

Page 2: 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.

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.

Page 3: 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.

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

Page 4: 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.

When lines are horizontal, their slopes are zero

Page 5: 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.

When lines are vertical, their slopes are undefined

Page 6: 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.

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!!!!

Page 7: 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.

Rally Robin

Determine whether each slope will be positive, negative, zero, or undefined

Page 8: 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.

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.

Page 9: 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.

The steeper the line, the higher the slope

Page 10: 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.

Now…. How to find the exact value of the slope

Rise/Run

Page 11: 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.

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.

Page 12: 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.

Slope Formula

Page 13: 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.

Examples:

Page 14: 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.
Page 15: 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.
Page 16: 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.
Page 17: 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.
Page 18: 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.

Sage n Scribe slope

Page 19: 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.

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

Page 20: 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.
Page 21: 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.

Now let’s try some practice in your textbook

• P. 142 (15-37) odd for practice

Page 22: 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.

Homework

• Page 142(16-38) even


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