To find the equation of a line perpendicular to the line given by the equation \( y = -3x + 5 \), we need to determine the slope of the original line and then use the negative reciprocal of that slope.
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Identify the slope of the original line: The equation \( y = -3x + 5 \) has a slope of \( -3 \).
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Find the negative reciprocal: The negative reciprocal of \( -3 \) is \( \frac{1}{3} \).
Therefore, any line that is perpendicular to \( y = -3x + 5 \) will have a slope of \( \frac{1}{3} \). The equation of a line in slope-intercept form ( \( y = mx + b \) ) can take the form \( y = \frac{1}{3}x + b \), where \( b \) can be any value (like 9 in the options).
Among the provided options, the correct one is: \( y = \frac{1}{3}x + 9 \) (this represents the line with slope \( \frac{1}{3} \) and a y-intercept of 9).
So the answer is: y = \( \frac{1}{3}x + 9 \)