Question 1184279
given:
({{{7}}},{{{-6}}})

{{{6x+5y=4}}}

perpendicular lines have slopes negative reciprocal to each other

so, first find a slope of the given line

{{{6x+5y=4}}}........solve for {{{y}}}

{{{5y=-6x+4}}}

{{{y=-(6/5)x+4/5}}}

=> slope {{{m=-(6/5)}}}
 negative reciprocal is {{{m=-1/(-(6/5))=5/6}}} -> a slope of the perpendicular line

use point-slope formula to find equation

{{{y-y[1]=m(x-x[1])}}}.........plug in {{{m=5/6}}} and coordinates of the point ({{{7}}},{{{-6}}})

{{{y-(-6)=(5/6)(x-7)}}}

{{{y+6=(5/6)x-7(5/6)}}}

{{{y=(5/6)x-7(5/6)-6}}}

{{{y=(5/6)x-71/6}}}


{{{ drawing( 600, 600, -10, 10, -10, 10, 
circle(7,-6,.12),locate(7,-6,p(7,-6)),
graph( 600, 600, -10, 10, -10, 10, (5/6)x-71/6, -(6/5)x+4/5)) }}}