Write a linear equation to find the temperature T at an elevation e on the mountain, where e is in thousands of feet.

Question

It is 76 degrees at the 6000-foot level of a mountain, and 49 degrees at the 12,000-foot level of the mountain. Write a linear equation to find the temperature T at an elevation e on the mountain, where e is in thousands of feet.

Answer 1

The linear equation is T = me + c   (m is slope and c is T intercept

 

76 = 6e + c   (1)

 

49 = 12e + c   (2)

 

from (1) c = 76 - 6e

 

substitute in (2) 49 = 12e +76 - 6e

 

6e = -27 ; e =- 27/6 = -4.5

 

therefore c = 76 -6(-4.5) = 103

 

T = -4.5e + 103   (remember e is in thousands of feet)