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📐 Mathematics  ·  Linear Inequalities  ·  JEE

The graph of 4x + 3y <= 12 in the first quadrant is bounded by the line through which two intercepts?

Answer: (3,0) and (0,4).

  • A (3,0) and (0,4)
  • B (4,0) and (0,3)
  • C (12,0) and (0,12)
  • D (3,0) and (0,3)

Correct answer: A. (3,0) and (0,4)

Explanation: Setting y=0 gives x=3; setting x=0 gives y=4. The intercepts are (3,0) and (0,4).

Number Line vs Half-Plane Representationx > 2 (open circle, hollow)2x ≤ 2 (closed circle, filled)shaded regionsatisfies the inequality2D inequality: dashed line = strict, shaded = solution side

One-variable inequalities use open (excluded) or closed (included) circles on a number line; two-variable inequalities use a dashed (strict) or solid (non-strict) boundary line, with the solution being the entire shaded half-plane on one side of it.

Concept context

Solving linear inequalities in one and two variables algebraically and graphically, and representing solutions on a number line or as a region in a plane.

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