To determine which of the given equations represents a line that is perpendicular to a specific function (not provided here), you need to consider the slope of the function being analyzed.
- Identify the slope of the function you have (let's say it's \( m \)).
- For a line to be perpendicular to it, its slope \( m' \) must satisfy the relationship \( m' = -\frac{1}{m} \).
Now let's analyze the slopes of the given equations:
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\( y = 2x - 1 \): The slope is \( 2 \).
- Perpendicular slope would be \( m' = -\frac{1}{2} \).
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\( y = -2x + 3 \): The slope is \( -2 \).
- Perpendicular slope would be \( m' = \frac{1}{2} \).
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\( y + 2 = 2(x - 4) \): This can be rewritten as \( y = 2x - 10 \). The slope is \( 2 \).
- Perpendicular slope would also be \( m' = -\frac{1}{2} \).
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\( x + 2y = 14 \): Rearranging gives \( 2y = -x + 14 \) or \( y = -\frac{1}{2}x + 7 \). The slope is \( -\frac{1}{2} \).
- Perpendicular slope would be \( m' = 2 \).
Based on the slopes identified, if the original function has a slope of \( 2\), then the lines that are perpendicular would need to have a slope of \( -\frac{1}{2} \). Therefore, the lines that match this condition would be:
- None of the options provided results in a slope of \( -\frac{1}{2} \).
However, if the original function has a slope of \( -\frac{1}{2} \), then the options with slopes of \( 2 \) (i.e., \( y = 2x - 1 \), \( y + 2 = 2(x - 4) \)) would be perpendicular.
To summarize, the selection of correct perpendicular line depends on the unprovided slope of the original function you refer to. If you have more information about the slope of that function, you can use this analysis to find the correct answer.