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The height of a widescreen monitor is proportional to its length. The table lists the length, l, and the height, h, of a few widescreen monitors.

Length, l (in inches) Height, h (in inches)
14.4 8.1
17.6 9.9
19.2 10.8
20.8 11.7
22.4 12.6
24.0 13.5

Which equation represents the proportional relationship between the lengths and heights of widescreen monitors?

1 answer

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:

  1. 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:

  1. 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:

\[ h = 0.5625l \]