Question 254318
for two lines to be perpendicular, their slopes have to have a product of -1

Find the slope of the first line
{{{2x + 3y  =  3 }}}
{{{3y = -2x + 3}}}
{{{y = -(2/3)x + 1}}} 
So the slope is {{{-2/3}}}

Find the slope of the second line
{{{2x + ky + 1  =  0}}}
{{{ky = -2x - 1}}}
{{{y = -(2/k)x -1/k}}}
So the slope of the second line is {{{-2/k}}}

Set the product of the two slopes equal to -1
{{{(-2/3) * (-2/k) = -1}}}
{{{4/3k = -1}}}
{{{k = -4/3}}}

Plot the graphs and verify
{{{graph(400,400,-10,10,-10,10, -2x/3 +1 , 3x/2 + 3/4)}}}