1. Finding the Rate of Change or Slope of Pipelines
“Fuel to the Future”
Finding the Rate of Change or Slope of Pipelines

2. *Instant Stars are number 4s!
Round Robin
Starting with the 1s and continuing clockwise, discuss the following two questions:
1. What are pipelines?
2. What are the many purposes of pipelines?
*Instant Stars are number 4s!

3. What are pipelines?
A pipeline is a long pipe, typically underground, for conveying oil, gas, etc, over long distances.
Most commonly liquids and gases are sent, but pneumatic tubes using compressed air can also transport solid capsules.
There are sewage, slurry, water, petroleum and even beer pipelines in existence today!

4. Why are pipelines important to you?
Pipelines are the energy lifelines of almost every activity of everyday life!
Do you enjoy taking a vacation?
You drive to the airport in your car. The gasoline and jet fuel traveled by pipeline.
Do you turn on the lights in your home?
The lamps use electricity, which is generated by burning natural gas or diesel fuel, which traveled by pipeline.
The list goes on and on!

5. Finding the Rate of Change or Slope of Pipelines
Pipelines near you might take product to the community next door to you, across the city, or across the state!
They have to change direction and slope based on the land where they are traveling.

6. Given a pipeline, how can you find the rate of change or the slope?
From a graph:
Make a stair between 2 points
Represent the change as:
Change in vertical axis (y)
Change in horizontal axis(x)
**Also known as rise/run
3) Write as unit rate
From a table:
Choose 2 points
Represent it as Change in Output
Change in Input
3) Put it in terms of unit rate
Given 2 points:
Point 1 (x1, y1) and Point 2 (x2,y2)
y2 -y1
x2 -x1

7. Find the Slope!
(-5, 3)
(7, -2)

8. Find the Slope!
Natural gas supplies 25 percent of all the energy Americans consume. It's our second largest source of energy. The table below shows the relationship between the number of miles traveled and the time it takes for the gas to be transported. Find the slope.
Miles (x)
Time in Minutes (y) 5 45 10 90 15
135 20
180

9. Find the Slope!
(2, 2)
(-2, -2)

10. Make your own problem up!
With your shoulder partner, write your own word problem involving finding the slope of a pipeline either using a table, graph, or two points.
Now trade with the pair across from you and solve it!

11. Exit Slip
Explain how to find the rate of change or slope given a table, graph, or two points.