What is the equation of the line that passes through (0,-1)(0,−1) and is perpendicular to the line that passes through the following points: (-5,11),(10,6) (−5,11),(10,6)?

1 Answer
sjc
Feb 25, 2017

y=3x-1y=3x−1

Explanation:

"the equation of a straight line is given by"the equation of a straight line is given by

y=mx+c" where m= the gradient & " c=" the y-intercept"y=mx+c where m= the gradient & c= the y-intercept

"we want the gradient of the line perpendicular to the line"we want the gradient of the line perpendicular to the line
"passing through the given points " (-5,11), (10,6)passing through the given points (−5,11),(10,6)

we will need " "m_1m_2=-1 m1m2=−1

for the line given

m_1=(Deltay)/(Deltax)=(y_2-y_1)/(x_2-x_1)

:.m_1=(11-6)/(-5-10)=5/-15=-5/15=-1/3

" "m_1m_2=-1=>-1/3xxm_2=-1

:.m_2=3

so the required eqn. becomes

y=3x+c

it passes through " "(0,-1)

-1=0+c=>c=-1

:.y=3x-1

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