Activities

1. Calculate the rate of change from the point (7, 2) to (10, -4).

2. Identify the rate of change and initial value from the table below.

3. Andrea started a babysitting service for her neighbors.  She babysat for the Andersons for three hours and made $34.  A couple nights later she babysat for the Chens and made $58 for six hours.  Construct a function to represent what Andrea charges for her babysitting service.
   
   
4. The following graph represents the cost of using a storage facility to keep your belongings.  Construct a function to represent the cost.  Show your work.

5. Miguel is preparing his family pool for some cleaning and repairs by draining all the water.  After two hours of draining the pool he still has 1,150 gallons left in the pool.  When he comes back after 12 hours of draining there is still 900 gallons to go.  What is the rate of change and initial value and what do they represent in this problem?  Write a function Miguel can use to figure out how long it will take to drain the pool.

Answer Key/Rubric

2. Rate of change =
   Initial value = (0, 7)

3. y = 8x + 10

4. y = 125x + 25
   Student work may include, but is not limited to:

• Find the slope/rate of change using the two given points: (1, 150) and (3, 400)

• Set up an equation to find the initial value

5. Explanations should be similar, but are not limited to:
   • Rate of change is which means the pool is losing water at a rate of 25 gallons an hour.
   • The initial value is (0, 1200) which means the pool started with 1200 gallons of water.
   • Function:  y = -25x + 1200