Exploring Lines and Characteristics of Slope

Slopes

Slope (or steepness) of lines is seen everywhere.
Engineers refer to the slope of a road as the grade. They often refer to the slope as a percentage.
Slope=riserun

Slope has no units since it is a ratio.

A grade of 8% would mean for every ran of 100 m, there is a rise of 8 m.
We use the letter m because in French the word for “to go up” is montor
The slope of a roof is known as the pitch

Example 1: Calculate the slope of each line segment

Solution:
mAB=riserun
=34
mCD=riserun
=-44
=-1
mEF=riserun
=04
=0
mHG=riserun
=50
=0
=undefined

Example 2: A line segment has one endpoint, A(4,7), and a slope of -23 . Find the coordinates of another possible endpoint, B.

Solution:
-Plot point A(4, 7)
-Use the slope
m=-23
A possible point is B(7,5)
OR
m=2-3
Another possible point is C(1,9)

Example 3: Draw lines with slopes of 1/2, 2, and -3.

Horizontal lines have a slope of 0.
Vertical lines have slopes which are undefined.

Note:
– A slope of -2 is the same as -21or2-1
– A slope of -23 is the same as -23or2-3
– A slope of 45 is the same as -4-5
– A line segment rising from left to right has a positive slope.
– A line segment falling left to right has a negative slope.