Help please, am really confused..........?

Question

hi i dont understand this problem can someone help me?

the relationship between celcius(c) and farenheit (f) degrees of measuring temperature is linear. Find an equation relating (c) and (f) degrees if 0(c) corresponds to 32(f) and 100(c) corresponds to 212(f). Use equation to find celcius measure of 70(f) degrees farenheit.

Thanks

Answer 1

A poorly worded problem, but easy to solve.

The linear relationship tells you that the the ratio of degrees between the c and f is the same anywhere on the temp scale

So we can easily figure out how 1 degree of one scale equates to the other scale:

0-100 c = 32-212 f

so 100 degrees of c = 180 degrees of f (212 minus 32)

divide both by 100

100/100=1 180/100 = 1.8

1 degree of c = 1.8 degrees of f

or divide both by 180

100/180=0.55  180/180 = 1

1 degree of f = .55 degrees of c

Now we need 1 more part - to compensate for the fact that one scale starts at 0 and the other at 32.  We want to know the temperature in terms of how many degrees above freezing on either scale

70 degrees f is 38 degrees above freezing (70 minus 32)

So now we know that each degree in f is equal to .55 degrees in c - so we do the math

38 * .55 = 21

So the formula is

(X-32) * .55 = Y  Where X is the degrees in Fahrenheit and Y is the degrees in Celsius

The Reverse is

(Y*1.8) -32=X

Multiplying the Celsius temp by 1.8 gives us the number of Fahrenheit degrees above freezing.  Then we add 32 to get the Fahrenheit temp

(21*1.8) + 32 = 70 (rounded up to the nearest whole degree)

Answer 2

So really you have two sets of points and you need to find the equation of the line that passes through them.  So you need to find the slope and then plug everything into the point-slope formula.  Here's the work....

x1 = 0 C

y1 = 32 F

x2 = 100 C

y2 = 212 F

m = (y2 - y1) / (x2 - x1) = (212 - 32)/(100 - 0) = 180/100 = 1.8

y - y1 = m(x - x1)

y - 32 = 1.8(x - 0)

y = 1.8x + 32

Remember, y = temp in Fahrenheit.  So we need to solve for x...

y = 1.8x + 32

y - 32 = 1.8x

x = (y - 32)/1.8

So that's your equation.  To use it to find out what 70 F is in C...

x = (70 - 32)/1.8 = 21.11

And doing a quick Google search, you can see that's correct.

Answer 3

Well, you could start by subtracting 32 from 212, then you see that the 100° Celsius range corresponds to a 180° Fahrenheit range. so 1&degF difference = 100/180 degree C.

Since the Fahrenheit range started at 32, you need to consider that in the conversion, 70°F is 70 - 32 = 38° higher than 32°F (which equals 0°C) multiplying 38 x 100/180 = 21.1°C