Solve the following inequality graphically in a two-dimensional plane: $5x + 2y \leq 10$.

(N/A) Step $1$: Consider the corresponding equation $5x + 2y = 10$.
Step $2$: Find the intercepts of the line. If $x = 0$,then $2y = 10$,so $y = 5$. The point is $(0, 5)$. If $y = 0$,then $5x = 10$,so $x = 2$. The point is $(2, 0)$.
Step $3$: Draw the line passing through $(0, 5)$ and $(2, 0)$. Since the inequality is $\leq$,the line is solid.
Step $4$: Test the origin $(0, 0)$. Substituting into the inequality: $5(0) + 2(0) \leq 10$,which is $0 \leq 10$. This is true.
Step $5$: Since the statement is true,the solution region is the half-plane containing the origin.