Question

Fine the slope of the line perpendicular to

Y=-1/2x -2

Answer 1

perpendicular slope = 2

Explanation:

the equation of a line in slope-intercept form is

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

y = -
`(1)/(2)` x - 2 is in this form

with slope m = -
`(1)/(2)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-1/2)` = 2

Answer 2

`\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=-(1)/(m_1)\\\\\text{We have}\ k:y=-(1)/(2)x-2\to m_1=-(1)/(2).\\\\\text{Therefore the slope of the line}\ l\ \text{perpendicular to the line}\ k\ \text{is:}\\\\m_2=-(1)/(-(1)/(2))=(1)/((1)/(2))=2\\\\Answer:\ \boxed{slope=2}`