Question

1. it is 76°f at the 6000 - foot level of a mountain, and 49°f at the 12,000 - foot level of the mountain. write a linear equation, in slope - intercept form, to find the temperature t at an elevation e on the mountain, where e is in thousands of feet. 14. use the equation in #13 to predict the temperature at an elevation of 20,000 feet.

Explanation:

Step1: Identify two points

We have points $(e_1,T_1)=(6,76)$ and $(e_2,T_2)=(12,49)$ since $e$ is in thousands of feet.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{T_2 - T_1}{e_2 - e_1}$. So $m=\frac{49 - 76}{12 - 6}=\frac{-27}{6}=-\frac{9}{2}$.

Step3: Find the y - intercept $b$

Using the slope - intercept form $T=me + b$ and the point $(6,76)$, we substitute: $76=-\frac{9}{2}\times6 + b$.
$76=-27 + b$, then $b = 76 + 27=103$.

Step4: Write the linear equation

The linear equation is $T=-\frac{9}{2}e+103$.

Step5: Predict the temperature at $e = 20$

Substitute $e = 20$ into the equation $T=-\frac{9}{2}\times20+103$.
$T=-90 + 103=13$.

Answer:

The linear equation for #13 is $T =-\frac{9}{2}e+103$.
The temperature at 20,000 feet for #14 is $13^{\circ}F$.