Ok here is the Problem.

Weather Temperature. The National Oceanic and Atmospheric ADministration (NO) has an online cconversion chart that relates degrees Fahrenheit to degrees Celsius. 77deg F is equevalent to 25deg C and 68deg F is equivalent to 20deg C. Assuming relationship is linear, write the equation relating degrees Celsius C to degrees Fahrenheit F. What temperature is the same in both degress Celsius and degress Fahrenheit?

Here steps I did:

77deg F = 25deg C

68deg F = 20deg C

Let x = Fahrenheit and y = Celsius

Linear Equation: y=mx + b or C = mF + b

Two Points of this Equation is (77,25), (68,20)

Solving the equation:

Calculate the change of rate:

$\displaystyle \frac {Y2 + Y1} {X2-X1}$

$\displaystyle m= \frac {25-20} {68-77} = \frac {-5} {-9} $

$\displaystyle m= \frac {-5} {-9} $

Subtitute the slope into the linear equation.

$\displaystyle m= \frac {-5} {-9} x + b $

finding b:

I use either point to satisfy the equation. I use (77,25)

Let x = 77

$\displaystyle

C = \frac {-5}{-9}F + b $

$\displaystyle

25= \frac {-5} {-9} (77) + b $

$\displaystyle

25= \frac {385} {9} + b $

$\displaystyle

b = \frac {160} {9}$

$\displaystyle Equation is : C = \frac {-5} {-9}F + \frac {160} {9} $

I don't know if i'm this right. I still haven't answer the other question: What temperature are both the same degrees.