C. Solving Problems with Linear Relations

C. Solving Problems with Linear Relations

Many relationships are linear and can be modelled using a linear equation or a linear graph. Use what you have learned so far in this lesson to explore the relationship between the Celsius and Fahrenheit temperature scales.

 

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There is a linear relationship between the Celsius and Fahrenheit temperature scales. The following table shows some equivalent temperatures.

1. Use the table to sketch a graph of the relation relating the Celsius and Fahrenheit scales.
   
   
   

2. 
   

   1. Estimate the slope and y-intercept of your graph.
      
      

   2. Determine an equation for the graph, in slope-intercept form.
      
      

   3. How did your estimated slope and y-intercept values compare to the calculated values?
      
      

3. 
   

   1. What does the slope represent in this scenario?
      
      

   2. What does the y-intercept represent in this scenario?
      
      
      

4. 1. What is 140ºC in Fahrenheit?
      
      

   2. What is –80ºF in Celsius?
      
      
      

5. Theoretically, the coldest possible temperature occurs at approximately -273.15°C and is sometimes referred to as “absolute zero”. Use this information to state the domain and range of the temperature conversion relation.

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