Question

need help with letter B and letter C in the pictures

Answer 1

B)

We will have that the linear relationship between Celcius and Fahrenheit can be written as follows:

*First: We will interpret the values at freezing and boiling temperature as coordinates, that is: (0, 32) & (100, 212). Now, we find the slope determine by these values and then replace them in the following expression:

$f-f_1=m(c-c_1)$

That is:

$m=\frac{212-32}{100-0}\Rightarrow m=\frac{9}{5}$

Now, that we have the slope, we will use one of the points (0, 32) and replace:

$f-32=\frac{9}{5}(c-0)\Rightarrow f=\frac{9}{5}c+32$

So, this is the function that describes the linear relationship between Celsius and Fahrenheit. [In the functions f & c stand for Fahrenheit and celsius respectively].

**

C)

We will find the temperature in which Fahrenheit and Celsius equal as follows:

We will write the relationship from "both sides" (When solved for Celsius and when solved for Fahrenheit):

$f=\frac{9}{5}c+32$

&

$c=(f-32)\cdot\frac{5}{9}$

Now, we can use any of the equations [Both represent the same function] and solve as follows:

$x=\frac{9}{5}x+32\Rightarrow-\frac{4}{5}x=32\Rightarrow x=-\frac{32\cdot5}{4}\Rightarrow x=-40$

[This is using the first equation]

$x=\frac{5}{9}(x-32)\Rightarrow x=\frac{5}{9}x-\frac{160}{9}\Rightarrow\frac{4}{9}x=-\frac{160}{9}$$\Rightarrow x=-\frac{160\cdot9}{9\cdot4}\Rightarrow x=-40$

[This is using the second equation]

So, at the temperature that they are the same is -40.