Question 1132462
When given the equation of the line that goes through ({{{6}}},{{{-10}}}) and is perpendicular to  {{{2y - 3x - 8 = 0}}}, find the value of y + (2/3)x - 4 ?????????=> it’s unclear what this means

you are given: the line that goes through ({{{6}}},{{{-10}}}) and is perpendicular to  {{{2y - 3x - 8 = 0}}}

so, all you can do is to find equation of that line


{{{2y - 3x - 8 = 0}}}...write it in slope intercept form

{{{2y =3x+ 8 }}}

{{{y =(3/2)x+ 4 }}}=> slope is {{{m=3/2}}}

perpendicular line will have a slope negative reciprocal which is {{{-2/3}}}

if the line that goes through ({{{6}}},{{{-10}}}), we can use point slope formula to find equation:

{{{y-y[1]=m(x-x[1])}}}

{{{y-(-10)=-(2/3)(x-6)}}}

{{{y+10=-(2/3)x-(2/3)(-6)}}}

{{{y=-(2/3)x+(2/cross(3))(cross(6)2)-10}}}

{{{y=-(2/3)x+4-10}}}

{{{y=-(2/3)x-6}}}


{{{drawing( 600, 600, -15, 15, -15, 15,
circle(6,-10,.12), locate(6,-10,p(6,-10)),
 graph( 600, 600, -15, 15, -15, 15, (3/2)x+ 4 , (-2/3)x-6)) }}}