Final answer:
The equation that expresses Katie's goal of learning new songs each week on her harp is S = 5 + 2W, where S represents the total number of songs she can play and W represents the number of weeks she has been learning.
Step-by-step explanation:
The equation that expresses Katie's goals is: S = 5 + 2W.
Here, S represents the total number of songs Katie can play, and W represents the number of weeks she has been learning. The constant term 5 represents the five songs she could already play, and the coefficient of 2 in front of W represents her goal to learn two new songs per week.
For example, if Katie has been learning for 3 weeks, the equation would be: S = 5 + 2(3) = 5 + 6 = 11. So after 3 weeks, Katie's goal would be to be able to play 11 songs.