Slopes Click to see more. What is Slope?
Slopes (or steepness) of lines are seen everywhere.
The steepness of the roof of a house is referred to as the pitch of the roof by home builders.
Malibu House
Ranch House
Ski Cabin
Give one reason why some homes have roofs which have a greater pitch. There is less snow build up in the wintertime.
Engineers refer to the slope of a road as the grade.
They often refer to the slope as a percentage.
Slopes and Lines run rise The slope of a line is the steepness of the line.
Slopes and Lines rise run
8 100 A grade of 8% would mean that for every run of 100 units, there is a rise of 8 units.
The steepness of wheelchair ramps is of great importance to handicapped persons. 1 12 The slope of wheelchair ramps is usually about If the rise is 1.5 m, what is the run? Ans: 18 m
Determine the slope of the line segment. 9 cm 5 cm We use the letter m because in French the word for “to go up” is monter. René Descartes (1596-1650) was from France and he was the first to define the Cartesian Plane.
Determine the slope (pitch) of the roof. Because the slope is a ratio, there are no units such as cm or cm2.
SLOPE
Determine the slope of the staircase. 2 3 3 3
Determine the slope of the line segment. y 7 4 x
Determine the slope of the line segment. y –5 7 x
Determine the slope of the line segment. y 6 Horizontal lines have a slope of zero. x
Determine the slope of the line segment. y 5 Vertical lines have slopes which are undefined. x
negative positive undefined zero
Determine the slope of the line segment y 5 40 = 8 x
Determine the slope of the line segment y –2 60 x
Draw a line which has a slope of
Draw a line which has a slope of –5 6 –5 6
Draw a line which has a slope of … b) 3 1 –3 3 1 1 –3 3 1
Find the slope of the line through (2,1) and (5,3)
Wouldn’t it be convenient if we could find the slope of a line without having to plot the points? We can if we use the slope formula . Slope Formula:
Use the slope formula to find the slope of the line through (2,1) and (5,3)
Use the slope formula to find the slope of the following line segments: 1) A (2, 4) to B (6, 7) 2) C (-3, 4) to D (1,-2) 3) E (-1,-4) to F (7,-8)