Public transit riders will see free access to the MBTA and the commuter rail for one day, while corporate and other passholders will see a 15 percent discount for one month, under a $5 million plan that state officials approved Wednesday.

The plan, passed unanimously by the board of directors of the Massachusetts Department of Transportation and the MBTA, seeks to make amends for a stretch of poor performance on the MBTA and the commuter rail as the public transit system endured a battery of winter storms.

The fare-free day will be Friday, April 24, according to an MBTA spokesman. The 15 percent discount is expected to take place during the month of May.

The combination of a free day and a one-month discount is "reasonable," said Transportation Secretary Stephanie Pollack.

Frank DePaola, who has been named the interim general manager of the MBTA, said the agency can handle the $5 million hit.

Gov. Charlie Baker, who said he encouraged the MBTA to consider rebates, reiterated his support in principle Wednesday before knowing the outcome of the board vote.

"There's also just a larger statement to made there about recognizing and appreciating the fact that's it's been a really tough couple of months for a lot of people who really depend on that system to live their lives, get to work and it's important for the Commonwealth, for the T, to acknowledge that," Baker said after speaking at a downtown Mass Insight Global Partnerships event.

Asked whether the financially challenged agency could afford to forego revenue, Baker said, "I think in some respects, that's the big question, but from my point of view it should be possible for the T to come up with an appropriate response to what's been an enormously difficult period of time for its riders and at the same time not put itself in a position where it busts the budget."