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.

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 rise run The slope of a line is the steepness of the line.

8 ft 100 ft A grade of 8% would mean for every rise of 8 feet, there is a run of 100 feet. = 8%

The steepness of wheelchair ramps is of great importance to those who use them. The slope of wheelchair ramps is usually about 1 foot rise for every 12 feet of run. 1 ft 12 ft If the rise is 2 feet, what is the run? Answer: 24 feet

3 m 5 m Determine the slope (pitch) of the roof. mmmm

Determine the slope of the staircase = 1

6 yd 3 sec Determine the slope. Distance (yards) Time (seconds) m = 6 yards 3 seconds m = 2 yds/sec

– 5 7 Determine the slope

7 Horizontal lines have a slope of zero Determine the slope.

6 Vertical lines have slopes which are undefined Determine the slope. cannot divide by zero!

positive negative zero undefined Summary: Types of Slopes

Slope Mountain Ski Resort Positive slope, + work Negative slope, - work Zero slope is zero fun! Undefined slope. Oh No!!!! T. Merrill 2005

Slope of line through 2 points To find the slope of a line through 2 given points we use the formula For example, Find the slope of a line that goes through (-3, 5) and (2, 18) x1x1 y1y1 x2x2 y2y

Determine the slope of this line = 8 How can you find slope when counting lines is just too much?

Let’s take a closer look... (7, 70) (2, 30) ΔxΔx ΔyΔy

In general, (x 2, y 2 ) (x 1, y 1 ) ΔxΔx ΔyΔy

Determine the slope of the line segment. (20, 7) (80, 5) x 1 y 1 x 2 y 2

Draw a line which has a slope of Draw a line which has a slope of 2

Draw a line which has a slope of –5 6 6

What Type of Slope is Shown? Positive Slope Negative Slope Zero Slope No Slope/Undefined

Slope of a Table In a table we can use the same formula. Pick any two pairs in the table for coordinates xy Pick any two rows. If it is linear it will be the same no matter which two rows you pick x1x1 x2x2 y1y1 y2y2

Conclusion Slope is: Describe the slope of each of the following the rate of change of a line Negative slope Undefined/ No slope Positive slope Zero/0 slope