Question: A gift shop sells stickers. The store sells 8 stickers for $3. Which of the following statements are true when $y$ represents the cost for purchasing $x$ stickers? Select all that apply. The rate of change is $\frac{8}{3}$. The slope of the equation is $\frac{8}{3}$. The rate of change is $\frac{3}{8}$. The slope of the equation is $\frac{3}{8}$. The unit rate is $\frac{3}{8}$ dollars per sticker. The constant of proportionality in this situation is $\frac{8}{3}$.

1. **State the problem:** We know the store sells 8 stickers for 3 dollars. We want to analyze the statements about the rate of change, slope, unit rate, and constant of proportionality when $y$ is the cost for $x$ stickers. 2. **Identify the variables and relationship:** - $x$ = number of stickers - $y$ = cost in dollars Since 8 stickers cost 3 dollars, the cost per sticker (unit rate) is: $$\text{unit rate} = \frac{3}{8} \text{ dollars per sticker}$$ 3. **Write the equation relating $y$ and $x$:** The cost $y$ is proportional to the number of stickers $x$: $$y = \frac{3}{8} x$$ Here, the slope (rate of change) is $\frac{3}{8}$. 4. **Analyze each statement:** - "The rate of change is $\frac{8}{3}$": **False** because rate of change is cost per sticker, which is $\frac{3}{8}$. - "The slope of the equation is $\frac{8}{3}$": **False** for the same reason. - "The rate of change is $\frac{3}{8}$": **True** because cost increases by $\frac{3}{8}$ dollars per sticker. - "The slope of the equation is $\frac{3}{8}$": **True** because slope equals rate of change in this linear equation. - "The unit rate is $\frac{3}{8}$ dollars per sticker": **True** by definition. - "The constant of proportionality in this situation is $\frac{8}{3}$": **False** because the constant of proportionality is the multiplier from $x$ to $y$, which is $\frac{3}{8}$. 5. **Final answers:** The true statements are: - The rate of change is $\frac{3}{8}$. - The slope of the equation is $\frac{3}{8}$. - The unit rate is $\frac{3}{8}$ dollars per sticker.