Question

Which line is perpendicular to the given equation: y=2x+17

Answer 1

Answer:

$\large\boxed{y=-\dfrac{1}{2}x+b,\ \text{wher}\ b\in\mathbb{R}.}$

Step-by-step explanation:

$\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\==========================\\\\\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\==========================\\\\\text{We have the equation of the line:}\ y=2x+17\to m_1=2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{2}.\\\\\text{The equation of a line:}\ y=-\dfrac{1}{2}x+b,\ \text{wher}\ b\in\mathbb{R}.$