How will the boundary line of (5x-2y\le 10) appear in the graph?

Correct answer: Solid line

The boundary is a solid line, so A is correct. To draw the boundary of 5x−2y≤10, first replace the inequality sign by equality: 5x−2y=10. Because the symbol is ≤, points on the boundary are included in the solution, so the line must be drawn solid. For comparison, a strict sign < or > excludes the boundary and uses a dashed line. B is therefore wrong because a dashed line represents exclusion. C is wrong because the boundary of a two-variable linear inequality is a complete straight line, not merely separate points. D is wrong because the equation clearly supplies a boundary line. A test point such as (0,0) can then identify the shaded side, although it does not change the solid nature of the line. Memory cue: inclusive signs ≤ and ≥ mean solid; strict signs < and > mean dashed.