The equation that represents the amount Emma earns (w) to the number of hours she worked (t) is:
w = 12.50t
This equation shows that Emma's earnings (w) are directly proportional to the number of hours she worked (t), with a proportionality constant of $12.50 per hour. If Emma works more hours, her earnings will increase proportionally, and if she works fewer hours, her earnings will decrease proportionally.