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Mathematics

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nikitadnepr [17]3 years ago

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I know the answer but first I need you to answer my math question

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What is the equation of the line that is perpendicular to y= -3x + 1 and passes through (2,3)?

Aleonysh [2.5K]

Answer:

$\large\boxed{y=\dfrac{1}{3}x+2\dfrac{1}{3}}$

Step-by-step explanation:

$\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=-3x+1\to m_1=-3.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-3}=\dfrac{1}{3}.\\\\\text{The equation of the searched line:}\ y=\dfrac{1}{3}x+b.\\\\\text{The line passes through }(2,\ 3).$

$\text{Put the coordinates of the point to the equation.}\ x=2,\ y=3:\\\\3=\dfrac{1}{3}(2)+b\\\\3=\dfrac{2}{3}+b\qquad\text{subtract}\ \dfrac{2}{3}\ \text{from both sides}\\\\b=2\dfrac{1}{3}$

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Take '1' away from one of them and give it to the other one.

You haven't changed their sum, but now they're<em> -12</em> and <em>-10 </em>.

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