Question

Which of the lines in the figure represents the relation between Celsius and Fahrenheit temperatures?

• A. $A$
• B. $B$
• C. $C$
• D. $D$

Answer 1

The correct option is A $A$

We know that relation between Celsius $\left(C\right)$ and Fahrenheit $\left(F\right)$ scales is given by
$\frac{C}{100}=\frac{F-32}{180}$
$\Rightarrow C=\frac{F}{180}\times 100-\frac{32}{180}\times 100$
$\Rightarrow C=\frac{5}{9}F-\frac{160}{9}$ ..........(1)
On comparing (1) with equation of straight line, $y=mx+c$,
Slope of line, $m=\frac{5}{9}$ which is positive
& $y$ intercept, $c=\frac{-160}{9}$ which is negative


We can see that the slope of line $A$ is positive and also its $y$ intercept is negative.
Therefore, line $A$ correctly represents the relation between Celsius and Fahrenheit temperatures.