Its 76 degrees fahrenheit at the 6000-foot level of a mountain, and 49 degrees fahrenheit at the 12000-foot level of the mountain. write a liner equation to find the temperature t at an elevation x on the mountain, where x is in thousands of feet.

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

Solution:

The linear equation in slope intercept form is given as:

T = cx + k ------ (i)

Where "t" is the temperature at an elevation x

And x is in thousands of feet

Given that its 76 degrees fahrenheit at the 6000-foot level of a mountain

Given, when c = 6 thousand ft and fahrenheit

This implies,

From (i)

76 = c(6) + k

76 = 6c + k

⇒ k = 76 - 6c  ----- (ii)

Given that 49 degrees Fahrenheit at the 12000-foot level of the mountain

Given, when c = 12 thousand ft and fahrenheit

This implies,

From (i)

49 = c(12) + k

49 = 12c + k

Substitute (ii) in above equation

49 = 12c + (76 - 6c)

49 = 12c + 76 - 6c

49 - 76 = 6c

6c = -27

Substituting the value of c in (ii) we get

Substituting the value of c and k in (i)

Where "x" is in thousands of feet

Thus the required linear equation is found

answer: it is 8

step-by-step explanation:

you know why its 8