Find the coordinates of the mid-point of the straight line joining the points of intersection of the curve and the line
The kind of obvious thing to do is to find the two point of intersection. From 2y+ 3x= 9, y= 9/2- (3/2)x. Replace y in and you get a quadratic equation for x which should have two solutions. Once you have found those two points of intersection, find the point midway between them.
Do you know that the point midway between and is ?