The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to $6 \,kg$. Read from the graph,the force required when the acceleration produced is $(i)$ $5 \,m/s^2$,$(ii)$ $6 \,m/s^2$.

(N/A) Let $y$ be the force and $x$ be the acceleration. Since force is directly proportional to acceleration,we have $y \propto x$,which implies $y = mx$,where $m$ is the constant mass.
Given $m = 6 \,kg$,the linear equation is $y = 6x$.
To draw the graph,we find some points satisfying the equation:

$x$ (Acceleration)	$0$	$1$	$2$
$y$ (Force)	$0$	$6$	$12$

Plotting the points $(0,0)$,$(1,6)$,and $(2,12)$ on a graph and joining them gives a straight line.
From the graph:
$(i)$ When acceleration $x = 5 \,m/s^2$,the corresponding force $y = 30 \,N$.
$(ii)$ When acceleration $x = 6 \,m/s^2$,the corresponding force $y = 36 \,N$.