SOLUTION: Water Freezes at 0 Celsius and 32 Farenheit. Water boils at 100 C and 212 F. A. Find the equation of the line that relates F to C. Use F=Y and C=X and you were given two points on

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Water Freezes at 0 Celsius and 32 Farenheit. Water boils at 100 C and 212 F. A. Find the equation of the line that relates F to C. Use F=Y and C=X and you were given two points on      Log On


   

Question 941098: Water Freezes at 0 Celsius and 32 Farenheit. Water boils at 100 C and 212 F.
A. Find the equation of the line that relates F to C. Use F=Y and C=X and you were given two points on the line, the first point is (0,32).
B. Use the equation to find F for C=16. Use the equation to find C for F=100.
C. At what temperature are farenheit and celsius the same (where does F=C)?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Water Freezes at 0 Celsius and 32 Farenheit. Water boils at 100 C and 212 F.
A. Find the equation of the line that relates F to C. Use F=Y and C=X and you were given two points on the line, the first point is (0,32).
:
Use the slope formula: m = %28%28y2-y1%29%29%2F%28%28x2-x1%29%29
Assign the x,y points as follows,
x1=0; y1=32
x2=100; y2=212
Find the slope (m)
m = %28%28212-32%29%29%2F%28%28100-0%29%29 = 180%2F100 = 9%2F5
y = mx + b, the slope intercept equation
When x=0, y=32, therefore b = 32
y = 9%2F5x + 32; is the equation
:
B. Use the equation to find F for C=16.
y = 9%2F5(16) + 32
y = 28.8 + 32
y = 60.8 degrees Farenheit
Use the equation to find C for F=100.
9%2F5x + 32 = 100
9%2F5x = 100 - 32
9%2F5x = 68
x = 5%2F968
x = 37.78 Celsius
;
C. At what temperature are Fahrenheit and Celsius the same (where does F=C)?
write the equation
y = 9%2F5y + 32
y - 9%2F5y = 32
-4%2F5y = 32
y = -5%2F4(32)
y = -40 degrees, F & C are the same