To find the point-slope form of the equation of the line, we need to identify the slope and a point on the line.
From the provided information, we know:
- The y-intercept is at (0, 2).
- The line is sloping down and to the right, which indicates a negative slope.
Based on the description, we can use point-slope form, which is given by:
\[ y - y_1 = m(x - x_1) \]
Where \((x_1, y_1)\) is a point on the line (in this case, (0, 2)) and \(m\) is the slope.
Let's identify the slope:
- From the y-intercept, we have the point (0, 2).
- The line slopes down and to the right, so we anticipate a negative slope value.
Now, let's look at the options provided to see which one can be in the format of the point-slope form using the point (0, 2).
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The option \(y + 2 = \frac{1}{2}(x - 1)\) does not pass through (0, 2) because if you plug in x = 0, the left side becomes -2 which does not satisfy the equation.
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The option \(y + 4 = \frac{1}{2}(x - 3)\) also does not pass through (0, 2).
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The option \(y = \frac{1}{2}x - 2.5\) cannot be a point-slope form as it is in slope-intercept form.
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Lastly, \(x - 2y = 5\) is not what we are looking for in point-slope form.
Since we need to establish the slope and use the point (0, 2), we find that none of these options are a valid point-slope in the form derived from our point. A normal point-slope equation would have looked like:
\[ y - 2 = m(x - 0) \]
If we evaluated the option related to y-intercept and the negative slope, we find that negative slopes (for this line) are necessary to make this a point of passage for (0, 2).
However, out of the available options, the closest option that represents a line correctly based on the y-intercept and line description seems unintuitive. Therefore, based on the typical graphical plotting, looking directly at slope analysis would value:
Final Answer: Based on the initial details provided that the y-intercept remains set as (0, 2), the ideal candidate must validate into the slope respectively. Without more concrete options at our disposal, errors restate within solving the existing line correctly may fall erroneous based on descriptive formatting defined by conventional plotting parameters.
Please ensure coordinates and plotted graphs guide choices accurately listing final analysis as negative inclination progressing negatively through y-values. Thus reflective confirming point-slope derivation affirmatively looks for accuracy in locating potential corrective linearity.
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