The function 𝑪 = 𝟎. 𝟓𝟓𝟔𝑭 − 𝟏𝟕. 𝟕𝟕𝟖 represents the relationship between degrees in Fahrenheit and in Celsius, where 𝑭 represents degrees Fahrenheit, and 𝑪 represents degrees Celsius. What does the slope represent in this function?
A. For every degree increase in Celsius, there is a 0.556 degree increase in Fahrenheit.
B. For every degree increase in Celsius, there is a 17.778 degree decrease in Fahrenheit.
C. For every degree increase in Fahrenheit, there is a 0.556 degree increase in Celsius.
D. For every degree increase in Fahrenheit, there is a 17.778 degree decrease in Celsius.
The slope of a linear function represents the rate of change between the two variables. In this case, the slope of the function is 0.556. This means that for every degree increase in Celsius, there is a 0.556 degree increase in Fahrenheit. Therefore, the correct answer is:
A. For every degree increase in Celsius, there is a 0.556 degree increase in Fahrenheit.
To determine what the slope represents in the function, we need to examine the coefficient of the 𝐹 term.
The given function is 𝐶 = 0.556𝐹 - 17.778.
The coefficient of the 𝐹 term is 0.556.
Therefore, the slope represents that for every degree increase in Fahrenheit, there is a 0.556 degree increase in Celsius.
So the correct answer is option C: For every degree increase in Fahrenheit, there is a 0.556 degree increase in Celsius.
To determine the meaning of the slope in this function, we need to understand how the function is defined and how it relates the values of Fahrenheit and Celsius. Let's break down the function given:
𝑪 = 𝟎. 𝟓𝟓𝟔𝑭 − 𝟏𝟕. 𝟕𝟕𝟖
Here, 𝑪 represents degrees Celsius, and 𝑭 represents degrees Fahrenheit. The function is linear, where the Celsius value is equal to 0.556 times the Fahrenheit value minus 17.778.
The slope of a linear function represents the rate of change between the two variables. In this case, the slope of the function is 0.556.
Now, let's interpret what this slope means in terms of the relationship between Fahrenheit and Celsius:
A. For every degree increase in Celsius, there is a 0.556 degree increase in Fahrenheit.
In an incorrect interpretation, this option suggests that the slope represents an increase in Fahrenheit with an increase in Celsius. However, since the slope is positive, it indicates an increase in Celsius leading to an increase in Fahrenheit, not the other way around.
B. For every degree increase in Celsius, there is a 17.778 degree decrease in Fahrenheit.
In an incorrect interpretation, this option suggests a negative slope value, indicating a decrease in Fahrenheit with an increase in Celsius. However, the given slope is positive, making this option inconsistent with the function.
C. For every degree increase in Fahrenheit, there is a 0.556 degree increase in Celsius.
In a correct interpretation, this option suggests that for every degree increase in Fahrenheit, there is a corresponding increase of 0.556 degrees Celsius. Since the slope is positive, this option aligns with the given function and correctly represents the relationship between the two variables.
D. For every degree increase in Fahrenheit, there is a 17.778 degree decrease in Celsius.
In an incorrect interpretation, this option suggests a negative slope value, indicating a decrease in Celsius with an increase in Fahrenheit. However, the given slope is positive, making this option inconsistent with the function.
Therefore, option C is the correct interpretation of the slope in this function.