Question 215483
Ok, you've got the slope of the new line correct.  The negative reciprocal of the given line which has a slope: {{{m = -3/2}}} is, of course, {{{2/3}}}
Now you can write:
{{{y = (2/3)x+b}}} In order to find b, the y-intercept, substitute the x- and y-coordinates of the point (3, 7) through which this line passes.
{{{7 = (2/3)(3)+b}}} Simplify.
{{{7 = 2+b}}} so...
{{{b = 5}}} 
The final equation is:
{{{highlight(y = (2/3)x+5)}}}