Question 261891
First, the slope, m, of a line that is perpendicular to the given line is the negative reciprocal of the slope of the given line. 
The slope of the given line is {{{m = 2/3}}}.
The slope of the new line will be {{{m = -3/2}}} so you can start with the slope-intercept form: {{{y = mx+b}}} but substitute {{{m = -3/2}}}
{{{y = (-3/2)x+b}}} Now substitute the x- and y-coordinates from the given point (2, -3) to find the value of b, the y-intercept.
{{{-3 = (-3/2)(2)+b}}} 
{{{b = 0}}} Now you can finish the equation in slope-intercept form:
{{{y = (-3/2)x+0}}} But you want integers only, so multiply through by 2 to get:
{{{2y = -3x}}} Finally, add 3x to both sides to get the standard form.
{{{highlight(3x+2y = 0)}}}