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What is the slope of the line perpendicular to $5x - 3y = 9$?

A) $3/5$
B) $-5/3$
C) $-3/5$
D) $5/3$

User SZT
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1 Answer

5 votes

Final answer:

The slope of the line perpendicular to 5x - 3y = 9 is found by taking the negative reciprocal of the original line's slope. The original line has a slope of 5/3, therefore, the perpendicular slope is -3/5, which is option C.

Step-by-step explanation:

The slope of the line represented by the equation 5x - 3y = 9 is found by first rewriting the equation in slope-intercept form which is y = mx+b, where m is the slope and b is the y-intercept. Solving for y, we get the equation y = \frac{5}{3}x - 3, which reveals that the slope of the original line is \frac{5}{3}.

To find the slope of a line perpendicular to the original line, we need to take the negative reciprocal of the original line's slope. The negative reciprocal of \frac{5}{3} is -\frac{3}{5}. Therefore, the slope of a line perpendicular to the given line is -\frac{3}{5}, which corresponds to option C.

User Scudsucker
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