The temperature T in Burrtown starts at 32°F in midnight when H=zero for the next few hours the temperature drops 2° every hour which equation represents the temperature t at hour h

Here we are given that at h=0 hours , the temperature is 32 F. The problem says that in every 1 hour, the temperature falls by 1 F. Hence at h=1 , the temperature will be 30F. If we consider hours h on x axis and temperature t on y axis , the coordinates will be (0,32) and (1,30).

Hence we have two coordinates of the line which represents the fall of the temperature with respect to the time.

Now we can use the two point form to find the equation of line passing through them.

The two point form is given as under

[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]

substituting the values we get

[tex]\frac{32-30}{0-1}=\frac{y-32}{x-0}\\\frac{2}{-1}=\frac{y-32}{x}\\-\frac{2}{1}=\frac{y-32}{x}\\-2x=y-32\\y=-2x+32\\[/tex]

Here our axes are in terms of h and t hence the equation will be

[tex]t=-2h+32[/tex]