Question

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

Answer 1

Answer: y = x + 6

Step-by-step explanation:

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

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

$m=-1$

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

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

$\frac{\left(-1\right)m_p}{-1}=\frac{-1}{-1}$

$m_p=1$

$\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$

$y=x+b$

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

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

$-2+b=4$

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

$-2+b+2=4+2$

$\text{Simplify}$

$b=6$

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

$y=x+6$