To write the linear function $f(x)$, we start by identifying the points given and determining the slope of the line. Here, $x$ represents the number of years since 2010, and $f(x)$ represents the number of yearbooks sold.

Step 1: Identify the points.

The two points given are:

• In 2010 ($x = 0$), $f(x) = 500$: $(0, 500)$
• In 2014 ($x = 4$), $f(x) = 1000$: $(4, 1000)$

Step 2: Find the slope $m$.

The slope formula is: $m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$ Substitute the given points: $m = \frac{1000 - 500}{4 - 0} = \frac{500}{4} = 125$

Step 3: Write the equation of the line.

The slope-intercept form of a linear equation is: $f(x) = mx + b$ Here, $m = 125$. We substitute one of the points, say $(0, 500)$, to find $b$: $f(0) = 125(0) + b \quad \Rightarrow \quad 500 = b$ Thus, the equation is: $f(x) = 125x + 500$

Final Answer:

The linear function is: $f(x) = 125x + 500$

Would you like more explanation or examples? Let me know!

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Here are 5 questions to expand your understanding:

1. How would the equation change if the number of yearbooks sold in 2016 was 1500?
2. What is the significance of the slope $m = 125$ in this context?
3. How many yearbooks would be sold in 2020 based on this function?
4. Can you graph this function and interpret its behavior?
5. How would you modify the function if sales started in a different year?

Tip: When identifying points for linear equations, always ensure the $x$-value reflects the correct reference (e.g., years since a starting point).