In certain​ conditions, the air temperature drops about 3.1F for each​ 1,000-foot rise in altitude.

Question

​(A) If the temperature at sea level is 74 ​F, write a linear equation that expresses the temperature T in terms of altitude A in thousands of feet.
​(B) At what altitude is the temperature 43​F?

Answer 1

(A) To express the temperature T in terms of altitude A in thousands of feet, we can use the slope-intercept form of a linear equation:

T = mx + b

Given that the air temperature drops about 3.1F for each 1,000-foot rise in altitude, the slope (m) of the equation will be -3.1. Since the temperature at sea level is 74 F, we can substitute this value into the equation and solve for the y-intercept (b):

74 = -3.1(0) + b
74 = b

Therefore, the linear equation that expresses the temperature T in terms of altitude A in thousands of feet is:

T = -3.1A + 74

(B) To find the altitude at which the temperature is 43 F, we can set T = 43 in the equation:

43 = -3.1A + 74

Rearranging the equation, we get:

-3.1A = 43 - 74
-3.1A = -31

Dividing both sides by -3.1, we find:

A = -31 / -3.1
A ≈ 10

Therefore, the altitude at which the temperature is 43 F is approximately 10,000 feet.