Question

Water freezes at 0 degrees Celsius and 32 degrees Fahrenheit. Water boils at 100 degrees Celsius and 212 degrees Fahrenheit.. . A. How would I write degrees Celsius as a linear function of degrees Fahrenheit?. . B. What is the slope of the linear equation and what does it mean?. . C. What is the y-intercept and what does it mean?

Answer 1

Degrees Celsius can be written as a linear function of degrees Fahrenheit using the equation C = (5/9)(F - 32), where the slope 5/9 indicates the rate of change between the two temperature scales, and the y-intercept represents the temperature in Celsius for a Fahrenheit temperature of zero.

Step-by-step explanation:

Linear Function of Degrees Celsius from Degrees Fahrenheit

To write degrees Celsius as a linear function of degrees Fahrenheit, we use the relationship between these two temperature scales. Knowing that water freezes at 0 degrees Celsius (which is 32 degrees Fahrenheit) and boils at 100 degrees Celsius (which is 212 degrees Fahrenheit), we can construct the linear equation. Since there are 180 Fahrenheit degrees for every 100 Celsius degrees, the rate of change is 5/9. Therefore, the equation can be written as:

C = (5/9)(F - 32)

Slope of the Linear Equation

The slope of the linear equation is 5/9, which indicates that a change of one degree Fahrenheit corresponds to a change of 5/9 of a degree Celsius. This slope represents the rate at which the two temperature scales increase with respect to each other.

Y-Intercept of the Linear Equation

The y-intercept of this linear function is -32. When we set Fahrenheit degrees (F) to 0, Celsius degrees (C) will equal -32 times the slope (5/9), which gives C = -160/9. The y-intercept represents the temperature in Celsius when the temperature in Fahrenheit is zero.

Answer 2

We are given with two conditions: after 0 degrees Celsius, this is equal to 32 degrees Fahrenheit and after at 100 degrees Celsius, this is equal to 212 degrees Fahrenheit . We translate these into points, we have (0,32) and (100, 212). we get the slope of the points ((212-32)/100) or 9/5. we plug to the equation y-y1 = m (x-x1) where m is equal to 9/5. y-32 = 9/5 (x-0). Simplifying, we get y -32 = 9x/5 or equal to y = 9/5 x + 32 where x is degrees Celsius and y is degrees Fahrenheit.