The table shows the temperature of a greenhouse where the temperature was taken after x hours.

Question

Greenhouse Temperature

Hour, x Temperature (ºF), y
0 50
5 60
8 66
9 68
13 76
15 80

When these data are graphed on a coordinate grid, the points all lie on the same line.

Complete the statements below about the data by selecting the correct choice from each drop-down menu.

The initial value, or y-intercept, of the linear function is ______ A. 10 B. 0 C. 50 D. 80, and represents the starting ___________ A. temperature in the greenhouse B. starting time of the experiment C. starting temperature outside __________ The rate of change is A. 10 B. 2 C. 5 D. 0.5 and represents ________________ A. and represents
an decrease of 2 degrees in temperature for each hour of time B. and represents an increase of 2 degrees in temperature for each hour of time C. and represents an increase of 0.5 degrees in temperature for each hour of time D. and represents an increase of 10 degrees in temperature for each hour of time

Answer 1

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.

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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.

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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.