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Find equation of a line perpendicular to the given line through the given point:
The line is $y=\frac{1}{2}x-2$
The point is $(3,6)$

I don't know what to do or try, please help me, its probably very easy to other people

Robert Howard
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aaly b
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    Until you learn LaTeX, you should use parentheses to make things clear. If you mean $\frac{1}{2}x-2$, you should write something like (1/2)(x)-2. If you mean $\frac{1}{2}(x-2)$ you should write (1/2)(x-2). – André Nicolas Jan 30 '14 at 05:45
  • I don't even know what your talkin about but is the answer y=2x+12 – aaly b Jan 30 '14 at 05:55
  • No it isn't. The slope of the given line is $\frac{1}{2}$, so the slope of the perpendicular is $-2$. The equation has therefore shape $y=-2x+b$. Put $x=3$, $y=6$. So $6=(-2)(3)+b$, and therefore $b=12$. So the equation is $y=-2x+12$. – André Nicolas Jan 30 '14 at 05:59
  • oh I thought I said that – aaly b Jan 30 '14 at 06:03
  • You left out the minus sign. – André Nicolas Jan 30 '14 at 06:04
  • oh okay thanks, I was wondering if you could help me on my newer math problem its a word problem please – aaly b Jan 30 '14 at 06:24

1 Answers1

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Slope of given line is : $m_1 = \frac{1}{2}$

If two lines are perpendicular, then the product of their slopes is $-1$. Exception being the lines are $x$ and $y$ axes which is not the case here. hence:

$$m_1*m_2 = -1$$ $$\frac{1}{2} * m_2 = -1$$ $$ m_2 = -2$$ Now calculate the line equation of line with slope = $-2$ and passing through point $(3,6)$. $$(y-6) = -2(x-3)$$ $$2x + y = 12$$ $$ y = -2x + 12$$

lsp
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