Question 1196328
the slope-intercept form of the equation of the line;

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

passes through ({{{2}}}, {{{-1}}}) 

perpendicular to {{{8x + 3y = 9}}}


first find the slope of given line

{{{8x + 3y = 9}}}

{{{  3y = -8x+9}}}

{{{  y = -(8/3)x+9/3}}}

{{{  y = -(8/3)x+3}}}

so, a slope is {{{m=-(8/3)}}}


recall that perpendicular lines have slopes negative reciprocal to each other, so the slope of the line perpendicular to given line will be

{{{m=-1/(-8/3)}}}

{{{m=3/8}}}


now use given point and a slope to find equation

{{{y-y[1]=m(x-x[1])}}}..........plug in the coordinates of the point ({{{2}}}, {{{-1}}}) and the slope {{{m=3/8}}}


{{{y-(-1)=(3/8)(x-2)}}}

{{{y+1=(3/8)(x-2)}}}

{{{y+1=(3/8)x-(3/8)2}}}

{{{y+1=(3/8)x-3/4}}}

{{{y=(3/8)x-3/4-1}}}

{{{y=(3/8)x-7/4}}}=> your line


{{{ drawing( 600, 600, -10, 10, -10, 10,
circle(2,-1,.12), locate(2,-1,p(2,-1)),

graph( 600, 600, -10, 10, -10, 10, -(8/3)x+3, (3/8)x-7/4)) }}}