Why are Indifference Curves always downwards sloping?Please explain with a graph and diagram and equation if possible

If a consumer equally prefers two product bundles, then
the consumer is indifferent between the two bundles. The consumer will get the same
level of satisfaction (utility) from either bundles.  The slope of indifference curve is
the rate at which a consumer is willing to trade one good for another, which is also
known as the marginal rate of substitution
(MRS).

1. Indifference curves are downward sloping.
   If the quantity of one goods is reduced, then you must have more of the other good to
   compensate for the loss.


2. Indifference curves are bowed
   inward (in most cases). The slope of indifference curves represent the MRS (rate at
   which consumers are willing to substitute one good for the other). People are usually
   willing to trade away more of one good when they have a lot of it, and less willingto
   trade away goods which are in scarce supply. This implies that MRS must increase as we
   get less of a good.

The marginal
rate of substitution (MRS) is the slope of the indifference curve. It is derived
mathematically for a non-linear indifference curve by taking the constant slope of the
straight-line tangent to the curve at the particular point of interest. Intuitively, the
absolute value of the MRS is the ratio between the marginal amount of good y that must
be given to compensate for a marginal loss of good x, and the marginal loss of good x.
The higher is the marginal utility of good x, the more utility is lost when good x is
taken away. The lower the marginal utility of good y, the moreof it must be given to
compensate for a given utility loss. Hence it is also intuitive that the MRS is the
ratio -MUx/MUy. The MRS changes along a non-linear indifference curve. For the
downward-sloping convex indifference curves which result from well-behaved preferences,
the MRS is always negative, and always decreases (becomes greater in absolute value) as
the amount of good x decreases.