Question

some1 help plz lol

The relationship between the Celsius (C) and Fahrenheit (F) scales for measuring temperature can be represented by a linear function. A temperature of 50 °F corresponds to 10 °C, and a temperature of 212 °F corresponds to 100 °C.

Which statement is the best interpretation of the slope of the graph of this function?

Question 1 options:

For each change of one degree in the Fahrenheit scale, there is a change of 59
5
9
degree in the Celsius scale.


A temperature of 0 °F corresponds to -17.78 °C.


A temperature of 0 °C corresponds to 32 °F.


For each change of one degree in the Fahrenheit scale, there is a change of 95
9
5
degree in the Celsius scale.

Answer 1

The slope is 9/5, this means that for each change in degree  in the Celsius scale there is a change of 9/5 degree in the Fahrenheit scale.

The y intercept is 32, this means that a temperature of 0 °C corresponds to 32 °F

A linear equation is given by:

y = mx + b

where y, x are variables, m is the slope of the graph and b is the y intercept.

Let F represent the temperature in Fahrenheit and C represent the temperature in Celsius.

50 °F corresponds to 10 °C it is given as (10, 50), while 212 °F corresponds to 100 °C, it is given as (100, 212). Hence:

$F-F_1=\frac{F_2-F_1}{C_2-C_1} (C-C_1)\\\\\\F-50=\frac{212-50}{100-10}(C-10) \\\\\\F-50=\frac{9}{5}(C-10) \\\\\\F=\frac{9}{5}C+32$

The slope is 9/5, this means that for each change in degree  in the Celsius scale there is a change of 9/5 degree in the Fahrenheit scale.

The y intercept is 32, this means that a temperature of 0 °C corresponds to 32 °F

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