Question

It is 64º F at the 5000-foot level of a mountain, and 48º F at the 10,000-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.

Answer 1

T = - 3.2e + 80

Explanation:

Given the following :

e = elevation in thousands of feets

T = temperature (°F)

e1 = 5 ; e2 = 10 (in thousands of feet)

T1 = 64° ; T2 = 48°

y = mx + c ; T = me + c

y = ; m = slope, c = intercept

64 = m5 + c - - - - (1)

48 = m10 + c - - - - (2)

From (1)

c = 64 - m5

Substitute c = 64 - m5 into (2)

48 = m10 + c - - - - (2)

48 = m10 + 64 - m5

48 - 64 = 10m - 5m

-16 = 5m

m = - 16 / 5

m = - 3.2

Substitute the value of m into c = 64 - m5

c = 64 - 5(-3.2)

c = 64 - (-16)

c = 64 + 16

c = 80

Inserting our c and m values into T = me + c

T = - 3.2e + 80

Where e is in thousands of feet

T is in °F