To find another equation that has the solution (6, 2) and is different from the line with slope \( \frac{2}{3} \) that goes through (6, 2), you can check which of the provided equations also passes through the point (6, 2).
We'll substitute \( x = 6 \) into each equation and see if \( y = 2 \) results.
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For \( y = \frac{2}{3}x - 1 \): \[ y = \frac{2}{3}(6) - 1 = 4 - 1 = 3 \quad (\text{not } (6, 2)) \]
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For \( y = -\frac{3}{2}x + 6 \): \[ y = -\frac{3}{2}(6) + 6 = -9 + 6 = -3 \quad (\text{not } (6, 2)) \]
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For \( y = \frac{1}{2}x - 1 \): \[ y = \frac{1}{2}(6) - 1 = 3 - 1 = 2 \quad (\text{is } (6, 2)) \]
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For \( y = 4x - 2 \): \[ y = 4(6) - 2 = 24 - 2 = 22 \quad (\text{not } (6, 2)) \]
The equation that also has the solution (6, 2) is: \[ \boxed{y = \frac{1}{2}x - 1} \]