To determine how much paint is needed for a wall with an area of 256 square feet, we can first identify the relationship between the area of the wall (x) and the amount of paint (y).
We notice that the problem states that the amount of paint varies directly with the area of the wall. This means we can express this relationship as:
\[ y = kx \]
where \( k \) is the constant of proportionality.
We can calculate \( k \) using the provided data points. Let's use the points (64, 4) and (144, 9) to find \( k \).
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For the point (64, 4): \[ k = \frac{y}{x} = \frac{4}{64} = \frac{1}{16} \]
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For the point (144, 9): \[ k = \frac{y}{x} = \frac{9}{144} = \frac{1}{16} \]
Since both calculations give the same value for \( k \), we can confidently say that:
\[ k = \frac{1}{16} \]
Now, we can use this value of \( k \) to find the amount of paint needed for a wall with an area of 256 square feet:
\[ y = kx = \frac{1}{16} \times 256 \]
Calculating that gives:
\[ y = \frac{256}{16} = 16 \]
Thus, the painter should expect to use 16 pints of paint to cover a wall with an area of 256 square feet.
The answer is: 16 pints.