After beginning a part-time job, a high school student decided to begin saving money in a savings account. She began by saving the same amount each month, until she received a raise after completing $7$ months at this job. She then decided to increase her savings per month for each month after that. The equation shown below describes her total savings, $ T $, in dollars after $ m $ months of working at this job, where $ m\geq 7 $.
$$ T = 50m + 25 (m - 7) $$
Which of the following is a correct statement about this equation?