Shelly uses up a $$ 350-\mathrm{ml} $$ bottle of shampoo in 7 months. What is the Slope $$ = $$ What is the unit rate $$ = $$ Write the equation $$ = $$ The time $$ t=3 $$ months, Shampoo $$ = $$. How long would it takes to use $$ 250 \mathrm{ml}= $$

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Let's break down each part of the problem step by step.

### 1. **Slope**

The **slope** in this context represents the rate at which Shelly uses the shampoo over time. It can be calculated using the formula:

$$
\text{Slope} = \frac{\text{Total Shampoo Used}}{\text{Total Time}} = \frac{350\, \text{ml}}{7\, \text{months}} = 50\, \text{ml/month}
$$

**Slope = 50 ml/month**

---

### 2. **Unit Rate**

The **unit rate** is essentially the same as the slope in this scenario. It tells us how much shampoo is used per single unit of time.

**Unit Rate = 50 ml per month**

---

### 3. **Equation**

To express the relationship between the amount of shampoo used and time, we can use a linear equation. Let $$ S(t) $$ represent the amount of shampoo used in milliliters after $$ t $$ months.

$$
S(t) = (\text{Slope}) \times t = 50t
$$

**Equation: $$ S(t) = 50t $$**

---

### 4. **Shampoo Used After 3 Months**

To find out how much shampoo Shelly has used after 3 months, substitute $$ t = 3 $$ into the equation:

$$
S(3) = 50 \times 3 = 150\, \text{ml}
$$

**Shampoo Used at $$ t = 3 $$ months = 150 ml**

---

### 5. **Time to Use 250 ml of Shampoo**

To determine how long it will take Shelly to use 250 ml of shampoo, set $$ S(t) = 250 $$ and solve for $$ t $$:

$$
250 = 50t \
t = \frac{250}{50} = 5\, \text{months}
$$

**Time to Use 250 ml = 5 months**

---

**Summary:**
- **Slope =** 50 ml/month
- **Unit rate =** 50 ml per month
- **Equation =** $$ S(t) = 50t $$
- **At $$ t = 3 $$ months, Shampoo Used =** 150 ml
- **Time to Use 250 ml =** 5 months
**Slope = 50 ml/month** **Unit Rate = 50 ml per month** **Equation: $$ S(t) = 50t $$** **Shampoo Used at 3 months = 150 ml** **Time to Use 250 ml = 5 months**

Shelly uses up a \( 350-\mathrm{ml} \) bottle of shampoo in 7 months. What is the Slope \( = \) What is the unit rate \( = \) Write the equation \( = \) The time \( t=3 \) months, Shampoo \( = \). How long would it takes to use \( 250 \mathrm{ml}= \)

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