To determine the point-slope form of the equation of the line described, we can use the given information:
- The line intercepts the y-axis at \((0, 2)\), which is the point where \(x = 0\) and \(y = 2\).
- The line is described as sloping down and to the right, which indicates a negative slope.
The point-slope form of a line is given by the equation:
\[ y - y_1 = m(x - x_1) \]
where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.
Since we know that the line intercepts at \((0, 2)\), we have \(x_1 = 0\) and \(y_1 = 2\).
Next, we need to determine the slope \(m\). However, since the options provided don't specify the slope explicitly, we'll analyze the slopes included in the choices:
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For the first option: \(y + 2 = \frac{1}{2}(x - 1)\)
- This suggests a point (1, 2) and slope of \(\frac{1}{2}\), not valid since it should be negative.
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For the second option: \(y + 4 = \frac{1}{2}(x - 3)\)
- This suggests a point (3, -4) and slope of \(\frac{1}{2}\), also not valid.
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For the third option: \(x - 2y = 5\)
- This doesn't match the point-slope form and is an alternative equation.
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For the fourth option: \(y = \frac{1}{2}x - 2.5\)
- This represents a line with positive slope and doesn't match what we expect.
Since we need a negative slope and the intercept is at \((0, 2)\), none of the given equations accurately reflect the situation. An appropriate equation using the point-slope form would resemble \(y - 2 = m(x - 0)\) for some negative slope \(m\).
Therefore, based on incomplete options for the specific situation, it appears all the provided responses are inaccurate given the details explained about the line.
If you require a specific choice from the options, please double-check the available choices or provide more context if any additional options are available.