Answer
a) $F$ in the $y$-direction, and $a$ in the $x$-direction.
b) The point $(0,0)$
c) $m\approx 0.56\;\rm kg$
Work Step by Step
a)
We know that the net force exerted on the cart is given by
$$F=ma$$
So the mass is
$$m=\dfrac{F}{a}$$
So to find the mass of the cart, we need to put the force in the vertical direction and the acceleration in the horizontal direction.
The output line's slope then will give us the mass of the cart.
$${\rm Slope}=\dfrac{F}{a}=m$$
b) Yes, we need to add the point $(0,0)$ since we know that the acceleration is zero when the force is zero and hence the slope is zero as well.
c) To find the best estimation of the mass of the cart, we need to draw the given dots and find the slope of the output line.
From the figure below, it is obvious that the mass of the cart is approximately 0.56 kg.
$$m=\color{magenta}{\bf 0.56}\;\rm kg$$