$\newcommand{\Var}{\operatorname{Var}} \newcommand{\Cov}{\operatorname{Cov}}$
If I'm given $\Var(\hat {\beta_1}-3\hat {\beta_2})$ how do I find the variance of this? I have gotten this far I'm just not sure about the covariance part. I know that $\Var(\hat {\beta_1}-\hat {\beta_2})=\Var(\hat {\beta_1})+\Var(\hat {\beta_2})-2\Cov(\hat {\beta_1},\hat {\beta_2})$ so I came up with the following: $\Var(\hat {\beta_1}-3\hat {\beta_2})=\Var(\hat {\beta_1})+9\Var(\hat {\beta_2})-{}???$ I thought it would be $6\Cov(\hat {\beta_1},\hat {\beta_2})$ but I'm just really not sure what I would do for the covariance part.