Question

at work, brett must check and record the internal temperature of the freezer on an hourly basis. when working properly, the temperature should remain constant over time. what word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly? zero positive undefined negative

Explanation:

Step1: Understand the relationship

The temperature \( T \) is a function of time \( t \), so we have \( T(t) \). When the freezer works properly, \( T \) is constant over time. So \( T(t) = c \) (where \( c \) is a constant) for all \( t \).

Step2: Recall the slope formula

The slope \( m \) of a line \( y = f(x) \) is given by \( m=\frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2 - x_1} \). For our function \( T(t) \), if we take two time points \( t_1 \) and \( t_2 \) (\( t_2>t_1 \)), then \( T(t_2)=c \) and \( T(t_1)=c \). So the change in temperature \( \Delta T=T(t_2)-T(t_1)=c - c = 0 \), and the change in time \( \Delta t=t_2 - t_1>0 \) (since \( t_2>t_1 \)). Then the slope \( m=\frac{\Delta T}{\Delta t}=\frac{0}{\Delta t}=0 \) (as long as \( \Delta t
eq0 \), which it isn't because \( t_2
eq t_1 \)).

Answer:

zero