Question

Draw a perpendicular to y=4x+6, and passing through(-8, -26) on a graph.

Answer 1

Answer:

$\mathrm{Perpendicular\:to\:}y=4x+6\mathrm{,\:and\:passing\:through\:}\left(-8,\:-26\right):\quad y=-\dfrac{1}{4}x-28$

Step-by-step explanation:

$\mathrm{Find\:the\:line\:}\mathbf{y=mx+b}\mathrm{\:perpendicular\:to\:}y=4x+6\mathrm{\:that\:passes\:through\:}\left(-8,\:-26\right)$

$\mathrm{Compute\:the\:slope\:of\:}y=4x+6$

$y=4x+6$

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

$m=4$

$\mathrm{Compute\:the\:slope\:of\:the\:perpendicular\:line}$

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

$\left(4\right)m_p=-1$

$\mathrm{Divide\:both\:sides\:by\:}4$

$\dfrac{4m_p}{4}=\dfrac{-1}{4}$

Simplify

$m_p=-\dfrac{1}{4}$

$\mathrm{Find\:the\:line\:with\:slope\:m=}-\frac{1}{4}\mathrm{\:and\:passing\:through\:}\left(-8,\:-26\right)$

$\mathrm{Compute\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:for\:slope\:m=}-\frac{1}{4}\mathrm{\:and\:passing\:through\:}\left(-8,\:-26\right)$

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

$\mathrm{Plug\:the\:slope\:}-\dfrac{1}{4}\mathrm{\:into\:}y=mx+b$

$y=\left(-\dfrac{1}{4}\right)x+b$

$\mathrm{Plug\:in\:}\left(-8,\:-26\right)\mathrm{:\:}\quad \:x=-8,\:y=-26$

$-26=\left(-\dfrac{1}{4}\right)\left(-8\right)+b$

$\mathrm{Isolate}\:b$

$-26=\left(-\dfrac{1}{4}\right)\left(-8\right)+b$

$\mathrm{Switch\:sides}$

$\left(-\dfrac{1}{4}\right)\left(-8\right)+b=-26$

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

$\dfrac{1}{4}\cdot \:8+b=-26$

$\dfrac{1}{4}\cdot \:8$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \dfrac{b}{c}=\dfrac{a\:\cdot \:b}{c}$

$=\dfrac{1\cdot \:8}{4}$

$\mathrm{Multiply\:the\:numbers:}\:1\cdot \:8=8$

$=\dfrac{8}{4}$

$\mathrm{Divide\:the\:numbers:}\:\dfrac{8}{4}=2$

$2+b=-26$

$\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}$

$2+b-2=-26-2$

$\mathrm{Simplify}$

$b=-28$

$\mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=-\dfrac{1}{4}\mathrm{\:and\:}\mathbf{b}=-28$

$y=-\dfrac{1}{4}x-28$