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

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Answer 1 · 2017-02-25T10:16:23

#y=3x-1#

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

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

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

we will need #" "m_1m_2=-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#