# PUGS is a rectangle. If the equation of PU is $y=\frac{2}{3x} + 4$. What is the slope of SP?

I don't get the answer to this problem, can somebody please tell me what the answer is.

• The line segments $SP$ and $PU$ are perpendicular (why?). Can you relate the slopes of perpendicular lines?
– user61527
May 16, 2014 at 0:58
• May 16, 2014 at 1:01

It might help to re-draw the rectangle so that it is slanted. Do you mean the equation of PU is y=2/3x+4? That means the slope is 2/3. Since SP is at a right angle to PU (it's a rectangle so it has to be), then it's slope is the negative reciprocal of that. That would be -3/2 (flip the fraction and multiply by -1), so the answer is C. Hope this helps.

• Try drawing it on graph paper with PU going up 2 and over 3, and it will be easier to visualize. May 16, 2014 at 1:11

Hint: Suppose some extension of a line segment has equation $y=mx+b$. Then any line that is perpendicular to this line (in other words, at a $90$ degree angle with it), has slope $-\frac{1}{m}$.

• Okay, I think its C, Is it? May 16, 2014 at 1:06
• Yes, the correct answer is C because this is the negative reciprocal of $\frac{2}{3}$. May 16, 2014 at 1:07

The answer is C, assuming that the equation of PU is $y = \frac{2}{3}x+4$.

• How do you solve it? I don't get it. May 16, 2014 at 1:06
• It is the negative reciprocal of 2/3. May 16, 2014 at 1:16
• Thanks a lot for your answer. May 16, 2014 at 1:28
• You're welcome. May 16, 2014 at 1:29