I hope this is in the right place.

Prove the following statement by a direct proof of the contrapositive statement.

If two lines are perpendicular, the product of their gradients is -1.

The contrapositive would be:

If the products of two gradients is not -1, then their lines are not perpendicular.

My problem is I don't know how to go about proving the statement.

I tried this:

$\displaystyle \tan (\theta-\phi)=\frac{\tan\theta-\tan\phi}{1-\tan\theta\tan\phi}$

$\displaystyle \tan\theta\tan\phi=1-\frac{\tan\theta-\tan\phi}{\tan (\theta-\phi)}$

$\displaystyle \frac{\tan\theta-\tan\phi}{\tan (\theta-\phi)}$ is not equal to 2

But I don't know how to continue.

Thanks