To find the equation that represents the proportional relationship between the lengths (l) and heights (h) of widescreen monitors, we start with the proportional relationship:
\[ h = k \cdot l \]
where \( k \) is the constant of proportionality.
To find \( k \), we can choose a pair of length and height from the table. For example, using the first pair:
- When \( l = 14.4 \), \( h = 8.1 \):
\[ k = \frac{h}{l} = \frac{8.1}{14.4} \approx 0.5625 \]
Now, using this value of \( k \), we can write the equation:
\[ h = 0.5625 \cdot l \]
To verify that this holds true for other pairs from the table, we can check one more pair:
- Using \( l = 20.8 \) and \( h = 11.7 \):
\[ k = \frac{h}{l} = \frac{11.7}{20.8} \approx 0.5625 \]
Since it gives us the same constant, we can reasonably conclude that the equation representing the proportional relationship between the lengths and heights of widescreen monitors is:
\[ h = 0.5625l \]