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Ahat [919]
2 years ago
14

Write an equation of the line that is perpendicular to the line y =

Mathematics
1 answer:
inn [45]2 years ago
6 0

Answer:

<h2>y = -3x + 3</h2>

Step-by-step explanation:

\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================

\text{We have the equation}\ y=\dfrac{1}{3}x+6\to m_1=\dfrac{1}{3}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{3}}=-3.\\\\\text{We have the equation}\ y=-3x+b.\\\\\text{Put the coordinates of the point}\ (2,\ -3):\\\\-3=-3(2)+b\\-3=-6+b\qquad\text{add 6 to both sides}\\3=b\to b=3\\\\\text{Finally:}\\\\y=-3x+3

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