Let's analyze the data provided in the table to determine the answers to the statements.
Finding the initial value (y-intercept):
From the data:
- At hour \( x = 0 \), the temperature \( y = 50 \)ºF.
So, the initial value, or y-intercept, of the linear function is C. 50, and it represents the starting A. temperature in the greenhouse.
Finding the rate of change:
To find the rate of change, we can examine the change in temperature over a specific time interval.
For instance:
- From \( x = 0 \) to \( x = 15 \): The temperature goes from \( 50 \)ºF to \( 80 \)ºF over \( 15 \) hours.
The change in temperature is: \[ 80 - 50 = 30 \text{ degrees} \]
The change in time is: \[ 15 - 0 = 15 \text{ hours} \]
Now, calculate the rate of change (temperature change per hour): \[ \text{Rate of change} = \frac{30 \text{ degrees}}{15 \text{ hours}} = 2 \text{ degrees per hour} \]
So, the rate of change is B. 2, and it represents B. and represents an increase of 2 degrees in temperature for each hour of time.
Final Answers:
- The initial value, or y-intercept, of the linear function is C. 50, and represents the starting A. temperature in the greenhouse.
- The rate of change is B. 2 and represents B. and represents an increase of 2 degrees in temperature for each hour of time.