To determine which line is perpendicular to the line \( y = 14x + 3 \), we look for a line with a slope that is the negative reciprocal of the slope of the given line.
The slope of the line \( y = 14x + 3 \) is \( 14 \). The negative reciprocal of \( 14 \) is \( -\frac{1}{14} \).
Now, let's check the slopes of the options provided:
- Option #1: \( y = 14x + 5 \) (slope = 14)
- Option #2: \( y = 4x + 5 \) (slope = 4)
- Option #3: \( y = -4x + 5 \) (slope = -4)
- Option #4: \( y = -14x + 5 \) (slope = -14)
None of the options provided have a slope of \( -\frac{1}{14} \). However, the line with the closest matching slope for perpendicularity should have a slope of exactly the negative reciprocal.
Since there isn't a direct match, none of these options represent a line that is perpendicular to \( y = 14x + 3 \) based on the typical requirements for perpendicular lines in a Cartesian plane. Should there be a misunderstanding or if the values should be reconsidered, please provide more context. Otherwise, the answer remains that none of the provided options are perpendicular to \( y = 14x + 3 \).
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