If yi = a + bxi: Mean(Y) = a + bMean(X), Var(Y) = $b^2$*Var(X), SD(Y) = |b|*SD(X). The additive constant a has NO effect on variance or SD — it shifts all values equally, leaving spread unchanged. The multiplicative constant b scales SD by |b| and variance by $b^2$. This property is heavily tested: "if each value is multiplied by 3 and then 5 is added, new variance = 9 * old variance."