The phrase "particular slant" refers to having a specific perspective or bias towards something. It means viewing something from a certain angle or with a particular opinion. Full definition
«The challenge», wrote Father Alexander Lucie - Smith in his Catholic Herald blog shortly after the Holy Father had announced his resignation, «will be in having to watch the airwaves fill with a whole load of people who are very marginal to Church life, and yet who will be invited to pontificate on all matters papal and religious, giving it their own particular slant, which they will advance as a mainstream view.» (faith.org.uk)
It is also clear, at least in William Carey's tract, «An Inquiry into the obligation of Christians to use means for the conversion of the heathens», which heavily influenced the missionary movement of the time, that Mark 16:15 was also drawn in and given a particular slant. (religion-online.org)
And he gives a particular slant to that observation when he writes: (religion-online.org)