The linear equation F=ac + b is used to change temperature from degrees
Celsius (°C) to degrees Fahrenheit (°F). Given that 0°C = 32°F and 100°C = 212°F,
calculate the constants a and b.
To calculate the constants a and b in the linear equation F = ac + b, we can use the given information about temperature conversions.
First, let's consider the conversion at 0°C = 32°F. Plugging these values into our equation, we get:
32°F = a(0°C) + b
Since multiplying a number by 0 yields 0, the equation simplifies to:
32°F = b
So, we know that the constant b is equal to 32.
Next, let's consider the conversion at 100°C = 212°F. Plugging these values into our equation, we get:
212°F = a(100°C) + 32
Simplifying further:
212°F = 100a + 32
Subtracting 32 from both sides of the equation:
180°F = 100a
Dividing both sides by 100:
1.8°F = a
Therefore, the constants for converting Celsius to Fahrenheit using the linear equation F = ac + b are a = 1.8 and b = 32.