1. Let's first understand the constraint given: $y - x$. This expression alone is not a complete constraint; typically, constraints are inequalities or equalities such as $y - x \leq c$, $y - x \geq c$, or $y - x = c$ for some constant $c$. 2. If the constraint is something like $y - x \leq 0$, then rearranging gives $y \leq x$. This means the feasible region includes points where $y$ is less than or equal to $x$. 3. When sketching the line $y - x = 0$, or equivalently $y = x$, the intercepts are at the origin $(0,0)$ for both $x$ and $y$ axes. This line passes through the origin and has a slope of 1. 4. If the constraint involves a constant that makes the intercept negative, for example $y - x \leq -1$, then the line is $y = x - 1$. This line intercepts the $y$-axis at $(0,-1)$, which is negative. 5. Having a negative intercept does not make the constraint infeasible. Feasibility depends on whether the region defined by the constraint intersects with the domain of the problem (e.g., non-negative $x$ and $y$ if those are required). 6. To check feasibility, consider the problem's domain and see if there exist points $(x,y)$ satisfying the constraint. For example, if $x \geq 0$ and $y \geq 0$, and the constraint is $y \leq x - 1$, then for $x=1$, $y \leq 0$ which is feasible at $y=0$. For $x=0$, $y \leq -1$ which is not feasible if $y$ must be non-negative. 7. Therefore, the feasibility of using the constraint depends on the problem's domain and the specific inequality or equality form of the constraint. In summary, a negative intercept in the constraint line does not automatically mean the constraint is not feasible. You must consider the entire feasible region and problem domain to determine feasibility.