10. The graph shows the amounts that you are collecting for selling calendars and boxes of greeting cards to raise money for the school band. a. Compare the steepness of the lines. What does this mean in the context of the problem? C. Find the slope of each line. What does each slope mean in the context of the problem?

To address your questions about the graph showing the amounts collected from selling calendars and boxes of greeting cards for the school band, let's break down each part: --- ### **a. Comparing the Steepness of the Lines** **Steepness Interpretation:** - **Steeper Line:** Indicates a greater rate of increase in the amount collected per unit (either per calendar or per box of greeting cards sold). - **Less Steep Line:** Indicates a slower rate of increase in the amount collected per unit. **Contextual Meaning:** - If, for example, the line representing **calendars** is steeper than the line for **greeting cards**, this means that each calendar sold contributes more to the total funds raised compared to each box of greeting cards sold. - Conversely, if the greeting cards' line is steeper, then selling each box of greeting cards raises more money than selling each calendar. **Visual Representation:** ``` Amount Collected | | / | / | / <- Steeper Line (e.g., Calendars) | / | / | / | / <- Less Steep Line (e.g., Greeting Cards) | |__________________________ Units Sold ``` --- ### **c. Finding the Slope of Each Line and Its Meaning** **Understanding the Slope:** - The **slope** of a line in this context represents the **amount of money collected per unit sold**. - **Mathematically**, slope is calculated as: \[ \text{Slope} = \frac{\text{Change in Amount Collected}}{\text{Change in Units Sold}} = \frac{\Delta \text{Amount}}{\Delta \text{Units}} \] **Calculating the Slope:** - **Identify Two Points** on each line (preferably where units sold are clear, such as (0,0) and another point like (units sold, amount collected)). - **Use the Slope Formula** to calculate for each product. **Example Calculation:** Suppose for Calendars: - Point 1: (0 calendars, $0) - Point 2: (50 calendars, $250) \[ \text{Slope}_{\text{Calendars}} = \frac{250 - 0}{50 - 0} = \frac{250}{50} = \$5 \text{ per calendar} \] For Greeting Cards: - Point 1: (0 boxes, $0) - Point 2: (40 boxes, $200) \[ \text{Slope}_{\text{Greeting Cards}} = \frac{200 - 0}{40 - 0} = \frac{200}{40} = \$5 \text{ per box} \] *Note: The above numbers are illustrative. Please use the actual data from your graph to compute the slopes.* **Contextual Meaning:** - **Calendars:** If the slope is \$5 per calendar, each calendar sold raises \$5 for the school band. - **Greeting Cards:** If the slope is \$5 per box, each box of greeting cards sold raises \$5 for the school band. **Interpreting Different Slopes:** - A **higher slope** means more money is raised per unit sold. - A **lower slope** means less money is raised per unit sold. --- ### **Summary** - **Steepness Comparison:** Determines which product raises more money per unit sold. - **Slope Calculation:** Quantifies the exact amount raised per unit, allowing for clear comparison and strategic planning (e.g., focusing on selling more of the higher-slope product). If you provide specific data points from your graph, I can assist you in calculating the exact slopes for each line.