Question 36327
Oh, Algebra is fun!!
(1) For the midpoint, we use the formula ((x1+x2)/2,(y1+y2)/2), which is basically taking the averages of the coordinates.  So here we have ((-3+6)/2,(-4-9)/2) = (3/2,-13/2).
(2) the slope is (change in y)/(change in x), or (y2-y1)/(x2-x1).  So here we have (-9+4)/(6+3) = -5/9.
(3) First, we need to finsdd the slope of our line, which means we need the slope of x+3y=4.  Writing this in slope-intercept form (y=mx+b) gives y=-x/3+4/3, which has a slope of -1/3.  So, a line perpendicular to this has a slope of 3.  Therefore, our line (through (-2,3) with slope 3) is y-3=3(x+2) (this is point-slope form), which in slope-intercept form is y=3x+9.