How do you write the equation of line passes through (-4,-3), and is perpendicular to 4x + y=7?

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Answer 1 · 2017-02-01T05:03:40

#3x-y+14=0#

Equation of a line that is perpendicular to #Ax+By=C#

is of the form #Bx-Ay=k# i.e. reversing te coefficients of #x# and #y# and changing sign of one of them.

Hence, the line perpendicular to #4x+y=7# has equation of the form

#x-4y=k# and as it passes through #(-4,-3)#

we should have #(-4)-4xx(-3)=k#

and therefore #k=-4+12=8#

and desired equation is #x-4y=8# or #3x-y+14=0#
graph{(x-4y-8)(4x+y-7)=0 [-10, 10, -5, 5]}