2.3.2 – Slope as Rate of Change
• In real life context, we can extend the idea of a
slope
• Remember, slope is a ratio; change in one set of
numbers over a change in another
• Average Rate of Change = the amount a quantity
changes, on average, to compared to a given
change in another quantity
– Dollars per hour
– Miles per hour
– Beats per minute
Determining x and y values
• When looking at some problems, we will have
to determine the values for x and y
– x (domain, input) = values we can change
ourselves such as time we take observations,
number of items we purchase, time of day or year
– y (range, outputs) = values we cannot change
ourselves; depends on another variable; price of
items, temperature, heights of objects
• Still calculate the rate of change the same as
the slope; just use the slope formula from
before
y 2  y1
• m=
x2  x1
• Example. Find the rate of change for the
points (4, 12) and (10, 20) where x is
measured as minutes and y is measured as
repetitions.
• Example. Find the rate of change for the
points (0, 25) and (9, 12) where x is measured
as days and y is measured as inches of water.
• When applying rate of change with word problems, the
process should go something like;
• 1) Identify x and y values (what you can change, what
you can’t change)
• 2) Write down what would represent x1, y1 and the
others
• 3) Use the slope formula to calculate rate of change
• 4) Reference the problem; does the math agree?
– If the problem needs a positive change, then your answer
should be positive or vice versa
• Example. The number of cell phone subscribers in
1985 was approximately 300,000 people in the US. In
2010, the number of subscribers was approximately
300,000,000. Find the average yearly rate of change
between 2010 and 1985.
• Example. The average high temperature in
Tallahassee during the month of July since
1899 is 92 degrees F. In December, the
average high temperature is 65 degrees F. Find
the average rate of change between the
months of July and December.
• Example. On a particular ski trail, over a 120 feet
horizontal distance, the elevation (or vertical
distance) goes from 4,690 feet to 4,240 feet. Find the
average rate of change over the duration of the trail.
(Remember, slope is the change in vertical over
change in horizontal).
• Assignment
• Pg. 83
• 39-43 odd, 46, 47, 48, 51, 52, 58