Given the equation $F=\frac{9}{5} C+32$ where $C$ is the temperature in degrees Celsius and $F$ is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:
$\left(20, F_1\right) \cdot\left(-30, F_2\right)$
Step 1 of 2: Compute the missing $y$ values so that each ordered pair will satisfy the given equation.
Answer (1)
Substitute C = 20 into the equation F = 5 9 C + 32 to find F 1 .
Calculate F 1 = 5 9 ( 20 ) + 32 = 68 .
Substitute C = − 30 into the equation F = 5 9 C + 32 to find F 2 .
Calculate F 2 = 5 9 ( − 30 ) + 32 = − 22 .
The missing y values are F 1 = 68 , F 2 = − 22 .
Explanation
Understanding the Problem We are given the equation F = 5 9 C + 32 , which converts Celsius to Fahrenheit. We need to find the Fahrenheit values, F 1 and F 2 , that correspond to C = 20 and C = − 30 , respectively.
Calculating F1 To find F 1 , we substitute C = 20 into the equation: F 1 = 5 9 ( 20 ) + 32
Simplifying F1 F 1 = 5 9 × 20 + 32 = 5 180 + 32 = 36 + 32 = 68
Calculating F2 To find F 2 , we substitute C = − 30 into the equation: F 2 = 5 9 ( − 30 ) + 32
Simplifying F2 F 2 = 5 9 × ( − 30 ) + 32 = 5 − 270 + 32 = − 54 + 32 = − 22
Final Answer Therefore, the missing y values are F 1 = 68 and F 2 = − 22 .
Examples
This conversion formula is used daily in weather forecasting and in many scientific applications. For example, if a weather forecast predicts a temperature of 25 degrees Celsius, we can use the formula to convert it to Fahrenheit: F = 5 9 ( 25 ) + 32 = 45 + 32 = 77 degrees Fahrenheit. Similarly, in scientific experiments, temperatures are often measured in Celsius, but for communication with the general public, it's helpful to convert these to Fahrenheit for easier understanding. Knowing how to convert between Celsius and Fahrenheit is useful in many real-world situations, from cooking to traveling.
