Determine the Rate of Change and Initial Value

Compare the initial values of each function.

• The initial value of item I is greater than the initial value of item II.

• The initial value of item I is equal to the initial value of item II.

• The initial value of item II is greater than the initial value of item I.

Compare the initial values and rate of change of both functions.

• Both functions have the same initial value and rate of change.

• The functions have different initial values and different rates of change.

• The rates of change are the same, but the initial values differ.

• The initial values are the same, but the rates of change differ.

Compare the initial values of the functions.

• Both functions have the same initial value.

• The initial value of item I is greater than the initial value of item II.

• The initial value of item II is greater than the initial value of item I.

Which of the following statements correctly describes the item shown above?

• The items have different rates of change, and item I is steeper.

• The items have different rates of change, but have the same steepness.

• The items have different rates of change, and item II is steeper.

• The items have the same rate of change.

Compare the initial values and the rates of change.

• The functions have different initial values and different rates of change.

• The rates of change are the same, but the initial values are different.

• The functions have the same initial value, but the rates of change differ.

• The y-intercepts are the same, but the rates of change differ.

Which linear function has the greatest slope?

• A

• B

• C

• D

Compare the rates of change.

• The rate of change of item II is greater than the rate of change of item I.

• The rate of change of item I is greater than the rate of change of item II.

• Both items have the same rate of change.

Rate of change is also known as ...

• initial value

• slope

• algebra

• y-intercept

The bait and tackle shop rents fishing equipment. There is an inital fee for hooks and bait plus an hourly cost to rent fishing rods. The table shows the cost of renting a fishing rod. Determine and interpret the rate of change and initial value. Assume that the relationship between the two quantities is linear.

• 4, 35; The rate of change is $4 per hour. The initial value is $25.

• 7.5, 20; The rate of change is $7.50 per hour. The initial value is $20.

• 10, 26; The rate of change is $10 per hour. The initial value is $26.

• 12.5, 80; The rate of change is $12.50 per hour. The initial value is $80.

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8.5.I

Pete’s Boat Rental charges an initial fee to rent a boat, plus an hourly fee. The table shows the cost to rent a canoe. Determine the initial fee that Pete’s charges to rent a canoe. Assume that the relationship between the two quantities is linear.

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8.5.I