Consider the relationship between temperature measured in degrees Celsius (°C) and degrees Fahrenheit (°F) Class 9

Consider the relationship between temperature measured in degrees Celsius (°C) and degrees Fahrenheit (°F) Class 9

Question 1.

Consider the relationship between temperature measured in degrees Celsius (°C) and degrees Fahrenheit (°F), which is given by °C = a °F + b. Find a and b, given that ice melts at 0 degrees Celsius and 32 degrees Fahrenheit, and water boils at 100 degrees Celsius and 212 degrees Fahrenheit. (Hint: When °C = 0, °F = 32 and when °C = 100, °F = 212. Use this information to find a and b, and thus, the linear relationship between °C and °F.) Class 9

Solution:

When °C = 0, °F = 32, and

When °C = 100, °F = 212.

Substituting the values of °C and °F in °C = a °F + b, we get

0 = 32a + b ...(i)

100 = 212a + b ...(ii)

From (i),

b = -32a ...(iii)

Substituting b = - 32a in (ii), we get

100 = 212a + (-32a)

∴ 100 = 212a - 32a

∴ 100 = 180a

∴ a = $\frac{100}{180}=\frac{5}{9}$

Now, substituting a = $\frac{5}{9}$ in (iii), we get

b = - 32 × $\frac{5}{9}=-\frac{160}{9}$

∴ The value of a is -, and the value of b is $-\frac{160}{9}$.

∴ °C = $\frac{5}{9}$ F - $\frac{160}{9}$ represents the linear relationship between degrees Celsius (°C) and degrees Fahrenheit (°F).