C=5/9(F−32)

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true? A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. A temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only

B) II only

C) III only

D) I and II only

Guest May 8, 2019

edited by
Guest
May 8, 2019

#1**+2 **

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

(1) A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.

(2)A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

(3) A temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

The slope of this linear equation is 5/9

This means that for every increase in Celsius of 5 degrees, Fahrenheit increases by 9 degrees ⇒ (A)

Dividihg both quantities in A by 5......for every 1 degree increase in Celsius, Fahrenheit increases by (9/5) = 1.8 degrees

So (2) is true

Next....divide both quantities in (A) by 9 and we have that for every 5/9 of a degree change in Celsius, Fahrenheit changes by 1 degree

So ( 1) is also true

So... "D" is correct

CPhill May 8, 2019

#2**+3 **

Here is another way to figure out the answer:

C = \(\frac59\)(F - 32) = \(\frac59\)F - \(\frac{160}9\)

When F = 0 , C = \(\frac59\)(0) - \(\frac{160}9\) = - \(\frac{160}9\)

When F = 1 , C = \(\frac59\)(1) - \(\frac{160}9\) = \(\frac59\) - \(\frac{160}9\) Notice this value of C is \(\frac59\) more than it was when F was 0 .

When F = 2 , C = \(\frac59\)(2) - \(\frac{160}9\) = \(\frac59\) + \(\frac59\) - \(\frac{160}9\) Notice this value of C is \(\frac59\) more than the previous.

So a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius.

C = \(\frac59\)(F - 32)

\(\frac95\)C = F - 32

\(\frac95\)C + 32 = F

When C = 0 , F = \(\frac95\)(0) + 32 = 32

When C = 1 , F = \(\frac95\)(1) + 32 = \(\frac95\) + 32 Notice this value of F is \(\frac95\) more than the previous.

When C = 2 , F = \(\frac95\)(2) + 32 = \(\frac95\) + \(\frac95\) + 32 Notice this value of F is \(\frac95\) more than the previous.

So a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 9/5 degrees Fahrenheit. (And 9/5 = 1.8). In other words, a temperature increase of 9/5 degrees (not 5/9 degrees) Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

hectictar May 9, 2019