Linear Function Word Problems Independent Practice Worksheet ... - Free Printable

Let's solve each problem from the Linear Function Word Problems – Independent Practice Worksheet step by step. Since I can't view images directly, I'll interpret the problems based on your description and the text you've provided.

---

Problem 1:

> Jake has been measuring the length of his baby’s hair. The first time it was 1 cm long and after one month it was 3 cm longer. If the hair continues to grow at this rate, determine the function that represents the hair growth and graph it.

#### Step-by-step Solution:

- Initial length (at time 0 months): 1 cm
- After 1 month: 1 + 3 = 4 cm
- So, the hair grows 3 cm per month

This is a linear relationship:
- Let $ h(t) $ = hair length at time $ t $ (in months)
- Slope $ m = 3 $ cm/month
- Initial value $ b = 1 $ cm

So, the function is:
$$
h(t) = 3t + 1
$$

#### Graph:
- Plot points:
- $ t = 0 $, $ h = 1 $ → (0, 1)
- $ t = 1 $, $ h = 4 $ → (1, 4)
- $ t = 2 $, $ h = 7 $ → (2, 7)
- Draw a straight line through these points.

✔ Answer: $ h(t) = 3t + 1 $

---

Problem 2:

> Bobby fills a water tank at a rate of 0.12 mL in every minute. Create a hypothetical table of values for time and quantity. Determine the equation that represents the function and state it graphically.

#### Step-by-step Solution:

- Rate: 0.12 mL per minute
- Assume starts at 0 mL at time 0

Let $ V(t) $ = volume in mL after $ t $ minutes

$$
V(t) = 0.12t
$$

#### Table of Values:

| Time (min) | Volume (mL) |
|------------|-------------|
| 0 | 0 |
| 5 | 0.6 |
| 10 | 1.2 |
| 15 | 1.8 |
| 20 | 2.4 |

#### Graph:
- Plot points: (0,0), (5,0.6), (10,1.2), etc.
- Draw a straight line through origin with slope 0.12

✔ Answer: $ V(t) = 0.12t $

---

Problem 3:

> When Jacob digs the Earth’s temperature rises as he digs deeper. He digs the Earth 3 meters deep and the temperature at that depth is 8°C. For every 5 meters the temperature increases by 10°C. If the temperature continues to rise at this rate, determine the function that represents this relationship and graph it.

#### Step-by-step Solution:

We are given:
- At 3 meters, temperature = 8°C
- Every 5 meters → increase of 10°C → so rate = $ \frac{10}{5} = 2^\circ C/\text{meter} $

Let $ T(d) $ = temperature at depth $ d $ meters

But we don’t know the temperature at 0 meters. Let's find it.

From 3 meters → 8°C
Slope = 2°C/meter
So, going back up 3 meters:
Temperature at surface = $ 8 - 2 \times 3 = 8 - 6 = 2^\circ C $

So, initial temperature at depth 0 is 2°C

Thus, the function is:
$$
T(d) = 2d + 2
$$

Wait — let's double-check:

At $ d = 3 $: $ T(3) = 2(3) + 2 = 6 + 2 = 8 $ ✔

Yes, correct.

Alternatively, if we use point-slope form:
$$
T(d) - 8 = 2(d - 3) \Rightarrow T(d) = 2d - 6 + 8 = 2d + 2
$$

Same result.

#### Graph:
- Points: (0,2), (3,8), (5,12), (10,22)
- Straight line with slope 2

✔ Answer: $ T(d) = 2d + 2 $

---

Problem 4:

> Carol fills water bottles at a rate of 2 bottles every minute. Create a hypothetical table of values for time and quantity. Determine the equation that represents the function and graph it.

#### Step-by-step Solution:

- Rate: 2 bottles per minute
- Starts at 0 at time 0

Let $ B(t) $ = number of bottles filled in $ t $ minutes

$$
B(t) = 2t
$$

#### Table of Values:

| Time (min) | Bottles |
|------------|---------|
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |

#### Graph:
- Points: (0,0), (1,2), (2,4), ...
- Line through origin with slope 2

✔ Answer: $ B(t) = 2t $

---

Problem 5:

> William has been measuring his height. The first time he was 5 feet tall and after one year he was 5.1 feet tall. If his height continues to grow at this rate, determine the function that represents his height growth and graph it.

#### Step-by-step Solution:

- Initial height: 5 ft at age $ t = 0 $
- After 1 year: 5.1 ft → growth = 0.1 ft/year

So, linear function:
$$
H(t) = 0.1t + 5
$$
Where $ t $ is time in years, $ H(t) $ is height in feet

#### Graph:
- Points: (0,5), (1,5.1), (2,5.2), (3,5.3), ...
- Straight line with slope 0.1

✔ Answer: $ H(t) = 0.1t + 5 $

---

✔ Final Answers Summary:

| Problem | Function Equation |
|--------|-------------------|
| 1 | $ h(t) = 3t + 1 $ |
| 2 | $ V(t) = 0.12t $ |
| 3 | $ T(d) = 2d + 2 $ |
| 4 | $ B(t) = 2t $ |
| 5 | $ H(t) = 0.1t + 5 $ |

Each function is linear, and all graphs are straight lines.

---

📌 Tips for Graphing:

- Use graph paper or coordinate plane
- Label axes appropriately (e.g., time vs. height)
- Plot at least two points and draw a line
- Include the y-intercept (initial value)

Let me know if you'd like these graphs drawn or explained further!