Mathematics: Write an equation of the line that is perpendicular to the line y = 1 2 x + 8 that passes through the point (4,6)

Write an equation of the line that is perpendicular

Ответ:

paranoidbih

05.01.2022

$\large\boxed{y=-2x+14}$

Step-by-step explanation:

$\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=\dfrac{1}{2}x+8\to m_1=\dfrac{1}{2}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{The equation of the searched line:}\ y=-2x+b.\\\\\text{The line passes through }(4,\ 6).$