Question

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

Answer 1

Fixing some formatting:

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?

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

statement II: A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

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

Answer 2

evaluate each statement one by one.

statement I: A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of (5/9) degree Celsius. ---> take a look at the equation C= (5/9)(F−32). when you increase F by 1, how much does C increase by? you can try treating this equation as a y = mx + b form, where m is the rate of change, and thus the amount that C increases when F increases by 1.

statement II: to get Fahrenheit in terms of Celcius, solve the equation for F. from there, see how F changes when you increase C by 1.8. to do this, you can set C = 0, calculate F, and then change C to 1.8 and see how much F changes.

statement III: looking at your equation from statement II, how much does F change when C changes by 1? use the same logic as you did from the earlier parts.

once you've determined which statement(s) is/are true, see which answer choice corresponds.