The average rate of change is the "change in value over the change in time."
[tex]\dfrac{185000-123500}{5} = \dfrac{61500}{5} = 12300[/tex]
The house has increased in value at an average rate of $12,300/year.
Assuming the same rate of change, in seven years the value will increase by 7x12300:
[tex]185000 + 7(12300) = 185000+ 86100 = 271100[/tex]
The house should be worth about $271,100 in seven year from now.