A special case of a linear function occurs when we talk about direct variation. If the quantities x and y are related by an equation y − kx for some constant k ± 0, we say that y varies directly as x, or y is proportional to x. The constant k is called the constant of proportionality. Equivalently, we can write fsxd − kx, where f is a linear function whose graph has slope k and y-intercept 0. (a) As dry air moves upward, it expands and cools. If the ground temperature is 20°C and the temperature at a height of 1 km is 10°C, express the temperature T (in °C) as a function of the height h (in kilometers), assuming that a linear model is appropriate. (b) Draw the graph of the function in part (a). What does the slope represent?(c) What is the temperature at a height of 2.5 km?
A special case of a linear function occurs when we talk about direct variation. If the quantities x and y are related by an equation y − kx for some constant k ± 0, we say that y varies directly as x, or y is proportional to x. The constant k is called the constant of proportionality. Equivalently, we can write fsxd − kx, where f is a linear function whose graph has slope k and y-intercept 0.
(a) As dry air moves upward, it expands and cools. If the ground temperature is 20°C and the temperature at a height of 1 km is 10°C, express the temperature T (in °C) as a function of the height h (in kilometers), assuming that a linear model is appropriate.
(b) Draw the graph of the function in part (a). What does the slope represent?
(c) What is the temperature at a height of 2.5 km?
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