Question

What is an equation of the line perpendicular to y=-x-2 and through (-2, 4)?

I would really appreciate the help, I've been stuck on this problem for awhile.​

Answer 1

Answer: y = x + 6

Explanation:

`\mathrm{Find\:the\:line\:}\mathbf{y=mx+b}\mathrm{\:perpendicular\:to\:}y=-x-2\mathrm{\:that\:passes\:through\:}\left(-2,\:4\right)`

`\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}`

`m=-1`

`\mathrm{The\:perpendicular\:slope\:is\:the\:negative\:reciprocal\:of\:the\:given\:slope}`

`\left(-1\right)m_p=-1`

`(\left(-1\right)m_p)/(-1)=(-1)/(-1)`

`m_p=1`

`\mathrm{Compute\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:for\:slope\:m=}1\mathrm{\:and\:passing\:through\:}\left(-2,\:4\right)`
`\mathrm{Plug\:the\:slope\:}1\mathrm{\:into\:}y=mx+b`

`y=x+b`

`\mathrm{Plug\:in\:}\left(-2,\:4\right)\mathrm{:\:}\quad \:x=-2,\:y=4`

`4=\left(-2\right)+b`

`-2+b=4`

`\mathrm{Add\:}2\mathrm{\:to\:both\:sides}`

`-2+b+2=4+2`

`\text{Simplify}`

`b=6`

`\mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=1\mathrm{\:and\:}\mathbf{b}=6`

`y=x+6`