Which curve in the given figure depicts the relationship between...

The relationship between temperature in Celsius ($C$) and Fahrenheit ($F$) is given by the equation:

$C = \dfrac{5}{9}(F - 32)$

Expanding this equation, we get:

$C = \dfrac{5}{9}F - \dfrac{160}{9}$

Comparing this with the equation of a straight line $y = mx + c$ (where $y$ is $C$ and $x$ is $F$), we find:
Slope ($m$) = $\dfrac{5}{9}$ (which is positive)
$C$-intercept = $-\dfrac{160}{9}$ (which is negative)

To find the $F$-intercept, we set $C = 0$:
$0 = \dfrac{5}{9}(F - 32) \Rightarrow F = 32$ (which is positive)

A line with a positive slope, a negative $C$-intercept, and a positive $F$-intercept corresponds to curve $a$ in the given figure.