To find a point on the line represented by the equation \( y - 1 = \frac{2}{3}(x - 6.5) \), we can substitute the values from the given options into the equation and check if they satisfy it.
Starting with the equation:
\[ y - 1 = \frac{2}{3}(x - 6.5) \]
We rearrange it to find \( y \):
\[ y = \frac{2}{3}(x - 6.5) + 1 \]
Now, let's evaluate each of the given points:
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Point (1, 6.5): \[ y = 6.5, \quad x = 1 \] \[ 6.5 = \frac{2}{3}(1 - 6.5) + 1 \] \[ 6.5 = \frac{2}{3}(-5.5) + 1 \] \[ 6.5 = -\frac{11}{3} + 1 = -\frac{11}{3} + \frac{3}{3} = -\frac{8}{3} \] (Not satisfied)
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Point (-1, -6.5): \[ y = -6.5, \quad x = -1 \] \[ -6.5 = \frac{2}{3}(-1 - 6.5) + 1 \] \[ -6.5 = \frac{2}{3}(-7.5) + 1 \] \[ -6.5 = -\frac{15}{3} + 1 = -5 + 1 = -4 \] (Not satisfied)
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Point (-6.5, -1): \[ y = -1, \quad x = -6.5 \] \[ -1 = \frac{2}{3}(-6.5 - 6.5) + 1 \] \[ -1 = \frac{2}{3}(-13) + 1 \] \[ -1 = -\frac{26}{3} + 1 = -\frac{26}{3} + \frac{3}{3} = -\frac{23}{3} \] (Not satisfied)
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Point (6.5, 1): \[ y = 1, \quad x = 6.5 \] \[ 1 = \frac{2}{3}(6.5 - 6.5) + 1 \] \[ 1 = \frac{2}{3}(0) + 1 \] \[ 1 = 0 + 1 \]
Since the last equation holds true, the point (6.5, 1) lies on the line represented by the given equation.
Thus, the answer is \((6.5, 1)\).