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The function \( f(x) = 1.8x + 32 \) is used to convert temperature in Celsius, \( x \), to temperature in Fahrenheit, \( f(x) \).

What do the constant term and the coefficient of the variable term represent?

A. For every change of 1 degree in temperature in Celsius, the temperature in Fahrenheit changes by 1.8 degrees. The starting value of temperature in Fahrenheit is 32 degrees when the temperature in Celsius is 0 degrees.

B. For every change of 1 degree in temperature in Fahrenheit, the temperature in Celsius changes by 1.8 degrees. The starting value of temperature in Fahrenheit is 32 degrees when the temperature in Celsius is 0 degrees.

C. For every change of 1 degree in temperature in Celsius, the temperature in Fahrenheit changes by 1.8 degrees. The starting value of temperature in Celsius is 32 degrees when the temperature in Fahrenheit is 0 degrees.

D. For every change of 1 degree in temperature in Fahrenheit, the temperature in Celsius changes by 1.8 degrees. The starting value of temperature in Celsius is 32 degrees when the temperature in Fahrenheit is 0 degrees.

Answer :

The constant term (32) in the function represents the starting value of temperature in Fahrenheit when the temperature in Celsius is 0 degrees.

The coefficient of the variable term (1.8) represents the rate of change in temperature in Fahrenheit with respect to a change in temperature in Celsius. Specifically, it signifies that for every 1-degree change in Celsius temperature, the temperature in Fahrenheit changes by 1.8 degrees. This coefficient reflects the linear relationship between Celsius and Fahrenheit temperatures, demonstrating how they are related by a constant multiplier (1.8) in this conversion formula.

In more detailed explanation, the function \(f(x) = 1.8x + 32\) is used to convert temperatures from Celsius (x) to Fahrenheit (f(x)). The constant term, 32, is the key to understanding the starting point of the conversion. When the Celsius temperature is 0 degrees (x = 0), the equation simplifies to \(f(0) = 1.8 * 0 + 32\), which equals 32 degrees Fahrenheit. This aligns with the fact that 0 degrees Celsius is equivalent to 32 degrees Fahrenheit.

The coefficient of the variable term, 1.8, represents the rate of change between the two temperature scales. For every 1-degree change in Celsius (Δx = 1), the Fahrenheit temperature changes by 1.8 degrees. This coefficient reflects the slope of the linear relationship between Celsius and Fahrenheit temperatures. It illustrates how the two scales are related by a constant multiplier, making it possible to convert between them using this simple formula. So, as you increase or decrease the Celsius temperature by 1 degree, the corresponding change in Fahrenheit is always 1.8 times that, leading to a proportional conversion between the two temperature scales.

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