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To solve the problem, let's walk through it step by step.

### Problem Summary:
- **Starting point (2002):** 6.07 quadrillion BTUs.
- **Rate of increase:** 0.17 quadrillion BTUs per year.
- **Find:** An equation in **slope-intercept form** to describe the amount of renewable power \( P \) (in quadrillion BTUs) produced in year \( y \), for \( y \) between **2002 and 2005**.

---

### Step 1: Identify the form of the equation.
Slope-intercept form is:
\[
P = m y + b
\]
where:
- \( P \) is the output (amount of power in quadrillion BTUs).
- \( y \) is the input (year).
- \( m \) is the slope, representing the rate of increase (0.17 quadrillion BTUs per year).
- \( b \) is the y-intercept, representing the amount of power at the starting point (6.07 quadrillion BTUs in 2002).

---

### Step 2: Express the slope \( m \) and adjust the year input.
The **slope** is the rate of increase per year:
\[
m = 0.17 \quad \text{(quadrillion BTUs per year)}.
\]

Since the **starting point** is the year 2002, we need to **shift the input years** so that:
- \( y = 0 \) corresponds to **2002**.
- \( y = 1 \) corresponds to **2003**.
- \( y = 3 \) corresponds to **2005**.

Let’s rewrite the equation in terms of \( y - 2002 \), where \( y \) is the current year.

---

### Step 3: Write the equation in slope-intercept form.
For a year \( y \), the equation becomes:
\[
P = 0.17 (y - 2002) + 6.07.
\]

---

### Step 4: Simplify the equation.
Distribute the slope:
\[
P = 0.17 y - (0.17 \times 2002) + 6.07.
\]

Now calculate:
\[
0.17 \times 2002 = 340.34.
\]

Thus:
\[
P = 0.17 y - 340.34 + 6.07.
\]

Simplify:
\[
P = 0.17 y - 334.27.
\]

---

### Final Equation:
\[
P = 0.17 y - 334.27.
\]

This equation gives the amount of renewable power \( P \) (in quadrillion BTUs) for any year \( y \) between 2002 and 2005.

---

Do you have any questions, or would you like me to walk you through specific steps? Here are five related questions for deeper understanding:

1. How do we adjust for years when working with slope-intercept form?
2. Why do we distribute the slope when writing the final equation?
3. How can we verify the solution using specific years (e.g., 2002, 2005)?
4. What does the slope represent in real-world terms?
5. How would the equation change if the rate of increase were different?

**Tip:** Always shift your year input when the problem specifies a starting point that isn’t zero!

From 2002 to 2005, U.S. consumption of renewable energy increased an average of 0.17 quadrillion BTUs per year. About 6.07 quadrillion BTUs of renewable power were produced in the year 2002. Write an equation in slope-intercept form to find the amount of renewable power P in quadrillion BTUs produced in year y between 2002 and 2005.

Learn how to create a linear equation to model the growth of renewable energy in the U.S. from 2002 to 2005. This example uses the slope-intercept form to describe renewable power production with a step-by-step breakdown. Suitable for students in Grades 9-12.

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