Question

A graph is plotted taking $^{\circ }C$ along the Y-axis and $^{\circ }F$ along the X-axis. It is a/an:
A. Parabola
B. Straight Line
C. Ellipse
D. Circle

Answer 1

The temperature scale is calibrated at two fixed points, one is ice point of the water $\left( 0{}^\circ C \right)$ and another is boiling point of the water $\left( 100{}^\circ C \right)$. The linear equation is straight line.

Complete step by step solution:
The Celsius temperature range was originally defined by setting zero as the temperature at which water froze. Later Zero degrees Celsius also gets defined as the temperature at which ice melts. The end of the temperature was fixed at 100 degree Celsius at which water boils.

In Fahrenheit scale the upper end of the scale is fixed at temperature 212 degree Fahrenheit and the lower end of the scale is fixed at 32 degree Fahrenheit.
By using temperature scale analogy,
Let $C$ is the temperature in Celsius scale and $F$ is on Fahrenheit scale.
$\begin{aligned} & \Rightarrow \dfrac{C-0}{100-0}=\dfrac{F-212}{212-32} \\\ & \Rightarrow \dfrac{C}{100}=\dfrac{F-32}{180} \\\ & \Rightarrow \dfrac{C}{5}=\dfrac{F-32}{9} \\\ & \Rightarrow C=\dfrac{5}{9}F-\dfrac{160}{9}\ldots \ldots \left( i \right) \end{aligned}$
Comparing equation $\left( i \right)$with $y=mx+c$

The given relation between degree Celsius and degree Fahrenheit, the graph represents the straight line.

Note: The scale to measure temperature is calibrated at two fixed temperatures.
Doubling the temperature in Celsius doesn’t double the temperature in Fahrenheit.