Question 1196327

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 parallel lines have same  slopes, so the slope of the line perpendicular to given line will be

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


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=-(8/3)}}}


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

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

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

{{{y+1=-(8/3)x+16/3}}}

{{{y=-(8/3)x+16/3-1}}}

{{{y=-(8/3)x+13/3}}}=> 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, -(8/3)x+13/3)) }}}