I need help with finding the physical meaning of a slope.

Slope is the 'steepness' of the line, also commonly known as rise over run. We can calculate slope by dividing the change in the y-value between two points over the change in the x-value

Yes, it is possible to change the transitional kinetic energy of an object without changing its rotational energy. For example dropping a spinning ball into the side of the table, the ball will keep its rotational motion while its transitional kinetic energy is changing.