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Hello i need some help on this: Find the equation of the line which: passes through (3,4) and is perpendicular to y=x+2 the answer is y=-x+7 using y=mx+c i didn't have trouble solving parallels and straight lines but i couldn't get it here

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  • $\begingroup$ Do you know the relationship between slopes of perpendicular lines? $\endgroup$ – J. W. Tanner Apr 26 at 16:55
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If the line has to be perpendicular to $y=x+2$ it has to have a 90 degree angle to it. Because it is a line with slope 1, your equation has to have slope -1. So we have $y=-1x+n$.

Now it has to pass through point (3,4). If you put those x and y values in the equation, you get: $$4=-1*3+n$$ $$4=n-3$$ $$7=n$$ So we have $n=7$ and $m=-1$: $$y=-x+7$$

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  • $\begingroup$ How did u get -1 in the first slope? $\endgroup$ – Yoda Apr 26 at 17:17
  • $\begingroup$ There is a theorem in plane analytic geometry that says that two lines with slopes $m_1$ and $m_2$ are perpendicular if and only if $m_1\cdot m_2 = -1$ (with some waffling about lines parallel or perpendicular to the axes because then the slope is either 0 or infinite). If you don't know that theorem, you should review it and perhaps prove it for yourself. $\endgroup$ – NickD Apr 26 at 18:35
  • $\begingroup$ so the m2 is reciprocal to -1 for example if we have (y=-2x+c) we do -1/2? $\endgroup$ – Yoda Apr 27 at 7:12
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Two lines with slopes $m_1,m_2$ resp. are perpendicular if $m_1\cdot m_2=-1$.

The slope of the first line is $m_1=1$.

Therefore $$ m_2=\frac{-1}{1}\\ m_2=-1 $$

So the slope of the second line must be $-1$. Also the line passes through $(3,4)$. Now the equation can be easily found.

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