Given the equation [tex]F=\frac{9}{5} C+32[/tex] where [tex]C[/tex] is the temperature in degrees Celsius and [tex]F[/tex] is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:
[tex]\left(-10, F_1\right) \cdot\left(10, F_2\right)[/tex]
Step 2 of 2: Plot the resulting set of ordered pairs using your answers from Step 1.
Answer (1)
Substitute C = − 10 into the equation F = 5 9 C + 32 to find F 1 = 14 .
Substitute C = 10 into the equation F = 5 9 C + 32 to find F 2 = 50 .
The ordered pairs are ( − 10 , 14 ) and ( 10 , 50 ) .
Plot the points ( − 10 , 14 ) and ( 10 , 50 ) on a coordinate plane. The values are ( − 10 , 14 ) and ( 10 , 50 ) .
Explanation
Understanding the Problem We are given the equation that converts Celsius to Fahrenheit: F = 5 9 C + 32 . We need to find the Fahrenheit values F 1 and F 2 corresponding to C = − 10 and C = 10 , respectively. Then, we will plot the points ( − 10 , F 1 ) and ( 10 , F 2 ) .
Calculating F1 First, let's find F 1 by substituting C = − 10 into the equation: F 1 = 5 9 ( − 10 ) + 32
F 1 = − 18 + 32
F 1 = 14 So, the first ordered pair is ( − 10 , 14 ) .
Calculating F2 Next, let's find F 2 by substituting C = 10 into the equation: F 2 = 5 9 ( 10 ) + 32
F 2 = 18 + 32
F 2 = 50 So, the second ordered pair is ( 10 , 50 ) .
Plotting the Points Now we have the two ordered pairs: ( − 10 , 14 ) and ( 10 , 50 ) . To plot these points, we locate -10 on the x-axis (Celsius) and 14 on the y-axis (Fahrenheit) for the first point. For the second point, we locate 10 on the x-axis and 50 on the y-axis.
Final Answer The problem asks us to plot the resulting set of ordered pairs. The ordered pairs are ( − 10 , 14 ) and ( 10 , 50 ) .
Examples
Understanding the conversion between Celsius and Fahrenheit is useful in many real-life situations. For example, when traveling to a country that uses Celsius, you can convert the temperature to Fahrenheit to better understand how hot or cold it is. Similarly, scientists and engineers often need to convert between these two temperature scales in their work. The formula F = 5 9 C + 32 allows for quick and accurate conversions, which is essential in many applications.
