College Algebra CLEP Prep Practice Exam

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What is the equation of the line perpendicular to y=3x+2 and passes through the point (4, 2)?

y= -3x+6
y= 3x-6
y= -3x-2
y=3x+6

The correct answer is: y= -3x-2

A line is considered perpendicular when it intersects another line at a 90 degree angle. Therefore, the slope of a perpendicular line to y=3x+2 must be the negative reciprocal of the slope of y=3x+2. In this case, the slope of y=3x+2 is 3, so the slope of the perpendicular line would be -1/3. We can use this information to eliminate options A and B, as they do not have a slope of -1/3. Option D has a positive slope of 3, making it parallel to the given line instead of perpendicular. C is the only remaining option that has the correct slope and also passes through the given point (4,2), thus making it the correct equation of the line perpendicular to y=3x+2 and passing through the point (4,2).