The graph AB shown in figure is a plot of temperature of a body in degree celsius and degree fahrenheit, then

Relation between Celsius and Fahrenheit scale of temperature is $\frac{\mathrm{C}}{5} = \frac{\mathrm{F}-32}{9}$

$\Rightarrow$      $C = \frac{5}{9}F-\frac{160}{9}$

Equating above equation with standard equation of the line
                    y = mx + c, we get
Slope of the line AB is $m = \frac{5}{9}.$