Answer
Each tick mark on the x-axis represents $0.25$ units.
Work Step by Step
Slope is the rise over run (or rise divided by the run).
Having a slope of $-\dfrac{2}{3}$ means that the rise is $-2$ and the run is $3$.
The two points have unknown x-coordinates but their y-coordinates are known:
$(x_1, 3)$ and $(x_2, 2)$
The rise between the two points is $=2-3=-1$
The run is represented by $x_2-x_1$.
Thus, the slope is given by:
$=\dfrac{\text{rise}}{\text{run}}=\dfrac{-1}{x_2-x_1}$
The slope is $-\dfrac{2}{3}$.
Note that $\dfrac{-1}{1.5}=-\dfrac{1}{1.5}=-\dfrac{2}{3}$.
So you can have:
$\dfrac{-1}{x_2-x_1}=\dfrac{-1}{1.5}$
This means that
$x_2-x_1=1.5$
Note that there are six vertical tick marks from $(x_1, 3)$ to $(x_2, 2)$
These vertical tick marks must represent 1.5 units.
Divide $1.5$ units by 6 tick marks to have:
$=\dfrac{1.5\text{ units}}{6\text{ tick marks}}=0.25$ units per tick mark.
