Question

Fine the slope of the line perpendicular to Y=-1/2x -2

Answer 1

$\text{Let}\\\\k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have}\ k:y=-\dfrac{1}{2}x-2\to m_1=-\dfrac{1}{2}.\\\\\text{Therefore the slope of the line}\ l\ \text{perpendicular to the line}\ k\ \text{is:}\\\\m_2=-\dfrac{1}{-\frac{1}{2}}=\dfrac{1}{\frac{1}{2}}=2\\\\Answer:\ \boxed{slope=2}$

Answer 2

Answer:

perpendicular slope = 2

Step-by-step explanation:

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - $\frac{1}{2}$ x - 2 is in this form

with slope m = - $\frac{1}{2}$

given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-1/2}$ = 2