Question 211337
First find the slope of the given line:
{{{-2x+3y = 8}}} Add 2x to both sides.
{{{3y = 2x+8}}} Divide both sides by 2.
{{{y = (2/3)x+8/3}}} Compare this with the slope-intercept form:
{{{y = mx+b}}}
The slope is:{{{m = 2/3}}} If a line is perpendicular to this, its slope will be the negative reciprocal or {{{m = -3/2}}} so we can start with:
{{{y = (-3/2)x+b}}} Now we find b by substituting the x- and y-coordinates from the given point:
{{{-3 = (-3/2)(-2)+b}}}
{{{-3 = 3+b}}}
{{{b = -6}}}
The equation is:
{{{y = (-3/2)x-6}}}