Question

at 2:00 pm the temperature is $18^{circ}$f, at 10:00 pm the temperature is $-9^{circ}$f
what is the change in temperature from 2:00 pm to 10:00 pm?
$\square^{circ}$f
(there is a number line with -9, 0, 18 marked and an arrow from 18 to -9)

Explanation:

Step1: Recall the formula for temperature change

The change in temperature is calculated by subtracting the initial temperature from the final temperature. So, if the initial temperature is \( T_1 \) and the final temperature is \( T_2 \), the change \( \Delta T=T_2 - T_1 \).
Here, \( T_1 = 18^{\circ}\text{F} \) (at 2:00 PM) and \( T_2=- 9^{\circ}\text{F} \) (at 10:00 PM).

Step2: Substitute the values into the formula

\( \Delta T=-9 - 18 \)
To subtract a positive number, we can rewrite it as adding its opposite. So, \( -9-18=-9+(-18) \).
When adding two negative numbers, we add their absolute values and keep the negative sign. The absolute value of - 9 is 9 and the absolute value of - 18 is 18. So, \( 9 + 18=27 \), and since both numbers are negative, \( -9+(-18)=-27 \).

Answer:

\(-27\)