To determine the value of \( k \) for the horizontal shift of the demand curve, we need to analyze the shift from \( y = f(x) \) (the original curve) to \( y = f(x - k) \) (the shifted curve).
A rightward shift of the demand curve occurs when \( k \) is positive, and a leftward shift occurs when \( k \) is negative. Since the graph shows one line to the left (the original) and one line to the right (the shifted), we are interested in the horizontal distance between the two lines.
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If the first line represents \( y = f(x) \) and is positioned at, say, 20 units on the x-axis, and the second line representing \( y = f(x - k) \) is positioned at 30 units, the horizontal shift is 10 units to the right. In this situation, \( k = 10 \).
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If the shift is smaller or larger, we would adjust the value of \( k \) accordingly.
Based on your description indicating that one line is to the left and one is to the right, we can conclude that \( k \) must be the distance between the two lines in terms of their x-axis positions.
Without the specific coordinates, I will tentatively provide the most sensible answer:
If we assume the graph supports a shift of 10 units based on typical choices, then \( k = 10 \) would be a valid selection, as it represents a common horizontal shift in demand curves.
Thus, the answer is:
10