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You are trying to compare the Fahrenheit and Celsius scales and you have two examples: Temperature A is 50 degrees Celsius and 122 degrees Fahrenheit. Temperature B is 100 degrees Celsius and 212 degrees Fahrenheit. What graph models the relationship between the Fahrenheit and Celsius scales? What is an equation of the line in slope-intercept form?

Respuesta :

The graph that models the relationship between the Fahrenheit and Celsius scales is attached below.

An equation of the line in slope-intercept form is F= 9/5 C+ 32. 


I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

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carlosego
For this case, the first thing we must do is define variables.
 We have then:
 c: temperature in degrees celsius
 f: temperature in Fahrenheit
 The generic equation of the line is:
 [tex]f-fo = m (c-co) [/tex]
 Where, the slope is given by:
 [tex]m = \frac{f2-f1}{c2-c1} [/tex]
 Substituting values:
 [tex]m = \frac{212-122}{100-50} [/tex]
 Rewriting:
 [tex]m = \frac{90}{50} [/tex]
 [tex]m = \frac{9}{5} [/tex]
 We choose an ordered pair:
 [tex] (co, fo) = (100, 212) [/tex] Substituting values in the generic equation:
 [tex]f-212 = \frac{9}{5} (c-100) [/tex]
 Rewriting:
 [tex]f-212 = \frac{9}{5}c - 180 [/tex]
 [tex]f = \frac{9}{5}c - 180 + 212 [/tex]
 [tex]f = \frac{9}{5}c + 32 [/tex]
 Answer:
 An equation of the line in slope-intercept form is:
 [tex]f = \frac{9}{5}c + 32 [/tex]
 See attached image.
Ver imagen carlosego

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