To find the equation of the line of fit in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, follow these steps:

---

Step 1: Calculate the slope ($m$)

The formula for the slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the points $(x_1, y_1) = (2, 2485.6)$ and $(x_2, y_2) = (6, 1172.5)$:

$m = \frac{1172.5 - 2485.6}{6 - 2} = \frac{-1313.1}{4} = -328.275$

Thus, the slope $m = -328.275$.

---

Step 2: Use the slope to find the y-intercept ($b$)

The slope-intercept form is $y = mx + b$. Use one of the given points to solve for $b$. Let's use the point $(2, 2485.6)$:

$y = mx + b \implies 2485.6 = (-328.275)(2) + b$

Simplify:

$2485.6 = -656.55 + b$

$b = 2485.6 + 656.55 = 3142.15$

Thus, the y-intercept $b = 3142.15$.

---

Step 3: Write the equation

Substituting $m = -328.275$ and $b = 3142.15$ into the slope-intercept form:

$y = -328.275x + 3142.15$

---

Interpretation

The equation $y = -328.275x + 3142.15$ represents the relationship between the number of years since 2010 ($x$) and the corresponding value ($y$). The slope $m = -328.275$ indicates that for every additional year since 2010, the value decreases by approximately 328.275 units. The y-intercept $b = 3142.15$ is the estimated value when $x = 0$, or in the year 2010.

---

Would you like more detailed explanations or assistance with another step? Here are some related questions for exploration:

1. How do we graph this line using the given equation?
2. What is the value of $y$ in 2015 ($x = 5$) using this equation?
3. Can we determine when $y$ will reach zero?
4. How does the slope affect the trend in the data?
5. What is the importance of interpreting the y-intercept in real-world scenarios?

Tip: Always double-check calculations when interpreting slopes and y-intercepts for accuracy!