1. **Stating the problem:** We are given two sets of data representing height over time and asked to determine the best scale value $A$ for the height axis in the first graph and to suggest improvements for the second line graph. 2. **Understanding scale $A$:** The scale $A$ represents the unit distance between two main divisions on the height axis. To find the best $A$, we want the scale to fit the range of heights nicely without wasting space or compressing the data too much. 3. **First data set:** Heights are 16, 58, 4, and 38 meters. The maximum height is 58 m and minimum is 4 m. 4. **Choosing $A$:** The height axis should cover from 0 to slightly above 58 m for clarity. If each unit $A$ corresponds to a certain number of meters, then $3A$ (three units) should be close to or exceed the maximum height. 5. **Calculate $A$:** Since the graph shows 3 units on the height axis, set $3A \geq 58$. 6. **Solve for $A$:** $$3A \geq 58 \implies A \geq \frac{58}{3} \approx 19.33$$ 7. **Interpretation:** The best scale $A$ is about 19.33 meters per unit to cover the height range well. --- 8. **Second graph improvements:** Given the data: | Time (days) | Height (mm) | |-------------|-------------| | 0 | 0 | | 1 | 12 | | 2 | 16 | | 3 | 19 | | 4 | 17 | 9. **Suggested improvements:** - The vertical axis should reach 22 mm (slightly above max 19 mm) for clarity. - The vertical axis should be marked in equal steps (e.g., increments of 2 or 4 mm) rather than jumping from 0 to 12. - The units should be given on the horizontal axis (e.g., "Time (days)"). - There should be a key if multiple data sets are present (not strictly necessary here but good practice). 10. **Redrawing the graph:** - Vertical axis from 0 to 22 mm with equal increments. - Horizontal axis labeled "Time (days)" with values 0 to 4. - Plot points at (0,0), (1,12), (2,16), (3,19), (4,17) connected by lines. **Final answers:** - Best scale $A$ for the first graph is approximately $19.33$ meters per unit. - Improvements for the second graph include extending vertical axis to 22, equal step markings, labeling units on horizontal axis, and adding a key if needed.