Answer
$T = 104.5^{\circ}F$
Work Step by Step
We can write a linear equation in this form:
$T = mt+T_0$
$m$ is the slope of the line
$t$ is the time in hours after 8:05 am
$T_0$ is the temperature at 8:05 am
We can find the slope $m$:
$m = \frac{\Delta T}{\Delta t}$
$m = \frac{101.0^{\circ}F-97.0^{\circ}F}{12:05~pm-8:05~pm}$
$m = \frac{4.0^{\circ}~F}{4~hr}$
$m = 1.0^{\circ}F/hr$
We can write the linear equation:
$T = 1.0~t+97.0^{\circ}F$
3:35 pm is 7.5 hours after 8:05 am. We can find the temperature at 3:35 pm:
$T = 1.0~t+97.0^{\circ}~F$
$T = (1.0^{\circ}F/hr)(7.5~hr)+97.0^{\circ}~F$
$T = 104.5^{\circ}F$
