Question

Draw a line with slope m=4 and passing through (-1, -6) in a Cartesian plane

Answer 1

Answer:

$\mathrm{Line\:with\:slope\:m=}4\mathrm{\:and\:passing\:through\:}\left(-1,\:-6\right):\quad y=4x-2$

Step-by-step explanation:

$\mathrm{Compute\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:for\:slope\:m=}4\mathrm{\:and\:passing\:through\:}\left(-1,\:-6\right)$

$\mathrm{Compute\:the\:}y\mathrm{\:intercept}$

$\mathrm{Plug\:the\:slope\:}4\mathrm{\:into\:}y=mx+b$

$y=4x+b$

$\mathrm{Plug\:in\:}\left(-1,\:-6\right)\mathrm{:\:}\quad \:x=-1,\:y=-6$

$-6=4\left(-1\right)+b$

$\mathrm{Isolate}\:b$

$-6=4\left(-1\right)+b$

$\mathrm{Switch\:sides}$

$4\left(-1\right)+b=-6$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$-4\cdot \:1+b=-6$

$\mathrm{Multiply\:the\:numbers:}\:4\cdot \:1=4$

$-4+b=-6$

$\mathrm{Add\:}4\mathrm{\:to\:both\:sides}$

$-4+b+4=-6+4$

$\mathrm{Simplify}$

$b=-2$

$\mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=4\mathrm{\:and\:}\mathbf{b}=-2$

$y=4x-2$