Rate of Change a k a Slope Rate

Rate of Change a. k. a. Slope

Rate of Change of a Linear Relationship run rise Rate of Change = The rate of change (slope) of a linear relationship is the steepness of the line.

Rates of change 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 buildup in the wintertime.

Engineers refer to the rate of change of a road as the grade.

They often represent the rate of change as a percentage.

100 8 A grade of 8% would mean for every rise of 8 units there is a run of 100 units. Rate of change = = 8%

The steepness of wheelchair ramps is of great importance for safety. 1 12 Rate of change of wheelchair ramp = If the rise is 1. 5 m, what is the run? Answer: 18 m because

Determine the rate of change (pitch) of the roof. 5 m 3 m

Determine the rate of change of each staircase. 3 2 3 3

Determine the slope (rate of change) of the line segment. 5 cm 9 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 of the line segment. y 6 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 zero undefined

Determine the rate of change. E a r n i n g s Which points will you use to determine rise and run? 4 20 = $5/hr What does this rate of Number of Hours Worked change represent? The hourly wage