Slopes Click to see more. What is Slope?.

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Presentation transcript:

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)