If a star is hotter is the wavelength shorter and higher energy?

That is true, the hotter a star is the shorter of wavelength it emits and the higher. It also depends on the mass of the star because the bigger it is, the faster it fuses its hydrogen fuel. Faster burning of fuel means more energy is released and so results in higher temperatures.

Hope this helps! Good luck :)

Explanation:

The energy of the light from the star is dependent on the temperature of the star.  The higher the temperature the higher the energy.  As the energy of light increases, the wavelength shortens as there is an inverse proportion between the two.

you'd use the equation that establishes a relationship between  energy  and  wavelength, which looks like this

e=h⋅cλ, where

λ  - the wavelength of the photon; c  - the speed of light, usually given as  3⋅108m/s; h  -  planck's constant, equal to  6.626⋅10−34j s

plug the value you were given for the energy of the photon in the above equation to get the wavelength

e=h⋅cλ⇒λ=h⋅ce

λ=6.626⋅10−34js⋅3⋅108ms−1.257⋅10−24j=1.581⋅10−1m