8. KAYAK The cost $$ y $$ (in dollars) to rent a kayak is proportional to the number $$ x $$ of hours that you rent the kayak. It costs $$ \$ 27 $$ to rent the kayak for 3 hours. a. Write an equation that represents the situation. b. Interpret the slope. c. How much does it cost to rent the kayak for 5 hours?

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Let's solve each part of the problem step by step.

### **a. Write an equation that represents the situation.**

Since the cost $$ y $$ is **proportional** to the number of hours $$ x $$, we can express this relationship with the equation:

$$
y = kx
$$

where:
- $$ y $$ is the total cost in dollars,
- $$ x $$ is the number of hours,
- $$ k $$ is the **constant of proportionality** (i.e., the cost per hour).

**Given:** It costs \$27 to rent the kayak for 3 hours.

We can substitute these values into the equation to find $$ k $$:

$$
27 = k \times 3
$$

Solving for $$ k $$:

$$
k = \frac{27}{3} = 9
$$

**Therefore, the equation representing the situation is:**

$$
y = 9x
$$

### **b. Interpret the slope.**

In the equation $$ y = 9x $$:

- The **slope** is **9**.
- **Interpretation:** The slope represents the **cost per hour** to rent the kayak. Specifically, it costs **\$9 per hour** to rent the kayak.

### **c. How much does it cost to rent the kayak for 5 hours?**

To find the cost $$ y $$ for 5 hours ($$ x = 5 $$), substitute $$ x = 5 $$ into the equation:

$$
y = 9x = 9 \times 5 = 45
$$

**Therefore, it costs \$45 to rent the kayak for 5 hours.**

---

**Summary:**

a. The equation is $$ y = 9x $$.

b. The slope $$ 9 $$ represents the cost of \$9 per hour to rent the kayak.

c. Renting the kayak for 5 hours costs \$45.
a. The equation is $$ y = 9x $$. b. The slope $$ 9 $$ means it costs \$9 per hour to rent the kayak. c. Renting for 5 hours costs \$45.

KAYAK The cost (in dollars) to rent a
kayak is proportional to the number of
hours that you rent the kayak. It costs
to rent the kayak for 3 hours.
a. Write an equation that represents
the situation.
b. Interpret the slope.
c. How much does it cost to rent the
kayak for 5 hours?

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KAYAK The cost (in dollars) to rent a kayak is proportional to the number of hours that you rent the kayak. It costs to rent the kayak for 3 hours. a. Write an equation that represents the situation. b. Interpret the slope. c. How much does it cost to rent the kayak for 5 hours?