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

When lines are horizontal, their slopes are zero

When lines are vertical, their slopes are undefined

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!!!!

Rally Robin

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

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.

The steeper the line, the higher the slope

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

Rise/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

Examples:

Sage n Scribe slope

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

Now let’s try some practice in your textbook

• P. 142 (15-37) odd for practice

Homework

• Page 142(16-38) even