Scalars a and b acting on a random variable X as:

and act on a random variables variance as:

;

Why? Think about it this way. If you had the ages of 10 people, and you multiplied their ages by 2 and added 10 years, the 10 years isn't going to affect the variation because they have all been adjusted evenly by 10 years. What will affect their ages is multiplying by the 2, and the variance is adjust by the square of the scalar.