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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 to find the temperature tt at an elevation xx on the mountain, where xx is the height in feet. enter answers as decimals rounded to the 4 digits.

Answer :

Answer:

[tex]t(x) = 103 -0.0045x[/tex]

Step-by-step explanation:

We are given the following in the question:

Let the equation:

[tex]t(x) = a + bx[/tex]

be the linear equation that represent temperature at an elevation x.

Temperature at 6000-foot level = 76 f

[tex]76 = a + 6000b[/tex]

Temperature at 12000-foot level = 49 f

[tex]49 = a + 12000b[/tex]

Solving the two equation, we get,

[tex]76-49 = -6000b\\27=-6000b\\\\b = \dfrac{-27}{6000}\\\\b = -0.0045\\76 = a + (-0.0045)6000\\76 = a -27\\a = 76 + 27\\a =103[/tex]

Thus, we can write the linear equation as:

[tex]t(x) = 103 -0.0045x[/tex]

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