Final answer:
The equation showing the relationship between the number of hours since Emmy went to bed, x, and the temperature in Fahrenheit, y, is y = -2x + 9, which means the temperature drops by 2°F with each passing hour.
Step-by-step explanation:
The student is asked to write an equation that represents the relationship between the number of hours since Emmy went to bed (denoted as x) and the temperature in Fahrenheit (denoted as y), given that the temperature is dropping at a rate of 2°F each hour from an initial temperature of 9°F.
The linear equation that models this situation is y = -2x + 9. Here, the -2 represents the rate of change of temperature, indicating the temperature is dropping by 2 degrees per hour. The +9 represents the temperature in degrees Fahrenheit when x is zero, that is when Emmy went to bed.
For example, if we want to find the temperature after 3 hours, we plug in x = 3 into the equation:
y = -2(3) + 9
y = -6 + 9
y = 3°F
So, after 3 hours, the temperature would be 3°F.