To solve this problem, let's break it down step by step:

The situation:

• There is a $9 setup charge and an additional $3 for every 10 minutes of computer rental time.
• The goal is to:
  1. Identify the independent and dependent variables.
  2. Write the linear function.
  3. Answer how much time can be rented for $21.

Key observations:

1. Independent variable (Input):

   • Time (t) in minutes is the input since the rental cost depends on how long you rent the computer.

2. Dependent variable (Output):

   • Rental cost (r) in dollars is the output since it is determined by the time rented.

Thus, the correct choice is B: "The independent variable is time (t), and the dependent variable is rental cost (r)."

Writing the linear function:

1. The cost starts at a flat $9 setup fee, so this is the y-intercept.
2. For every 10 minutes, the cost increases by $3. This gives a rate of change (slope):
   • For 1 minute, the rate is $\frac{3}{10} = 0.3$ dollars per minute.

The linear function is: $r = 9 + 0.3t$

Solving for time when rental cost is $21:

1. Substitute $r = 21$ into the function: $21 = 9 + 0.3t$
2. Simplify: $21 - 9 = 0.3t \implies 12 = 0.3t$
3. Solve for $t$: $t = \frac{12}{0.3} = 40$

Final Answer:

• 40 minutes of computer time can be rented for $21.

Would you like further clarification or additional examples? Here are some related questions to deepen your understanding:

1. How can you rewrite the equation to express $t$ in terms of $r$?
2. What would the cost be for renting the computer for 25 minutes?
3. If the cost increases to $5 per 10 minutes, how would the equation change?
4. Why is it important to clearly distinguish between independent and dependent variables?
5. How would a graph of this function look, and what does its slope represent?

Tip: Always identify the slope and intercept when writing linear equations—they define the rate of change and the starting value!