For small changes in temperature, the formula for the expansion of a metal rod under a change in temperature is: $$g - L = a L (t - T),$$ where $g$ is the length of the object at temperature $t$ , and $L$ is the length at temperature $T$ , and $a$ is a constant which depends on the type of metal.

1. Express $g$ as a linear function of $t$ . Find the slope and vertical intercept in terms of $L$ , $T$ , and $a$.
slope =
intercept =

2. A rod is 90 cm long at 110 degrees F and made of a metal with $a=10^{-4}$. Write an equation giving the length of this rod at temperature $t$ (because $a=10^{-4}$ is very small, give an exact answer: do not round expand multiplied numerical products to get rounded decimals).
$g =$ cm

(What does the sign of the slope tell you about the expansion of a metal under a change in temperature?)