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a) Because we are assuming that T is a linear function of h, we can write

T = mh + b

We are given that T = 20 when h = 0, so

20 = m x 0 + b = b

In the other words, the y-intercept is b = 20

We are also given that T = 10 when h = 1, so

10 = m x 1 + 20

The slope of the line is m = 10 – 20 = -10 and the required linear function is

T = -10h + 20

b) The graph of the above equation is

The slope is m = -10^{0}c/km, and this represents the rate of change if temperature with respect to height

c) At a height of 1.5 km, the temperature is

T = -10 (2) + 20 = 0^{0}c

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