When you want to find an intersection between objects, all you are doing is finding where both of them are equal. If you get a contradiction of some sort (like 2 = 3 or 0 = 1), then it means there is no intersection, but if you get a value that makes sense (like x = 3, or y = 7) then that is where both objects meet.
So to get you started off lets look at the first scenario.
We have y = x and y = (-2/3)x + 5. If these two intersection it means they both must be equal and have the same x and y values and if this is the case then y = y for bot expressions which means we have x = (-2/3)x + 5 since an intersection means that both y's and x's are going to be equal for the intersected point.
So based on this, can you now solve for your unknown x value and get the remaining y value to get the point of intersection?