Slack lines put anchors under gigantic loads via the following equation:
Load = 1/2 * (Wt of person + slackline)/COS(1/2 * Catenary Angle),
where
Catenary Angle = 180 degrees for a perfectly flat slackline under load
As Catenary Angle approaches 180 degrees (taughter slackline), COS (1/2 * 180) = 0, so Load on the anchor goes to infinity.
If your Weight is 1 kn (224 lbs), and
Load at Failure for a 1 biner anchor = 22 kn, then your Catenary Angle is
Angle = 2 * ACOS(1/2 * 1 /22) = 177 degrees
If the gate was somehow kinked open, your biner breaking strength drops to 8 kn
Angle = 2 * ACOS (1/2 * 1/8) = 172 degrees
If you want a 3x factor of safety for a single biner anchor at this weight, then you need a Catenary Angle that is no larger than:
Angle = 2 * ACOS (1/2 * 1*3/22) = 172 degrees
BTW, the shorter the line, the less spring deflection you've got, the closer the Catenary Angle gets to 180 degrees, and the larger the loads. Longer slack lines, despite adding the extra weight of the rope, generally have lower anchor loads.
You might consider using big stainless locking biners for slacklining rather than those light weight jobbies. Don't use clove hitches for attachments either. They can get so tight you've got to chop the tat/rope to get them off. Rewoven figure 8 is good.