Rate of Change

1
Rate of Change

• Learning Goal
• To find the slope (rate of change) of any line
  using rise and run.
• To apply that knowledge to real life situations

2
Rate of Change of a Linear Relationship
The rate of change of a linear relationship is
the steepness of the line.
3
Rates of change are seen everywhere.
4
The steepness of the roof of a house is referred
to as the pitch of the roof by home builders.
5
Give one reason why some homes have roofs which
have a greater pitch.
There is less snow buildup in the wintertime.
6
Engineers refer to the rate of change of a road
as the grade.
7
They often represent the rate of change as a
percentage.
8
A grade of 8 would mean for every rise of 8
units there is a run of 100 units.
8
9
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
10
Determine the rate of change (pitch) of the roof.
3 m
5 m
11
Determine the rate of change of each staircase.
12
Determine the rate of change.
Which points will you use to determine rise and
run?
Earnings
4
20
5/hr
What does this rate of change represent?
Number of Hours Worked
The hourly wage
13
Determine the rate of change.
2
Which points will you use to determine rise and
run?
Earnings
40
20/hr
What does this rate of change represent?
Number of Hours Worked
The hourly wage
14
Determine the rate of change.
Which points will you use to determine rise and
run?
Distance
-30
6
-5 km/h
What does this rate of change represent?
Number of Hours
Speed and direction
15
Determine the rate of change.
Which points will you use to determine rise and
run?
Distance
6
0
What does this rate of change represent?
Number of Hours
Speed and direction
16
Summary Types of Slopes

• Positive Slope
• Negative Slope
• Zero Slope
• Undefined Slope
• Slopes in General

Homework 5.3.1 Ramps, Roofs, and Roads Handout
on slopes
17
Exit Ticket Draw 2 lines on each graph a) one
line with a slope greater than 2 and another line
that has a negative slope. Show your calculations
to prove that both of your lines meet these
conditions. b) one line with a slope of zero,
and one with a variable slope.