Straight Lines

A line crossing both axes bounds a right triangle with the axes whose legs are the magnitudes of the x- and y-intercepts, so finding those intercepts immediately gives the area. Setting y = 0 in 4x + 3y - 24 = 0 gives 4x = 24, so x = 6, the x-intercept. Setting x = 0 gives 3y = 24, so y = 8, the y-intercept. The triangle has legs 6 and 8 along the axes, so its area is (1/2)(6)(8) = 24 square units. Option 48 forgets the factor of one-half. Option 12 halves one leg erroneously. Option 36 mistakes the legs as 6 and 12. This applies the standard JEE Advanced intercept-triangle area method. Plausibility check: the right angle sits at the origin between the positive intercepts 6 and 8, and (1/2)(6)(8) = 24 is consistent with a moderate triangle entirely in the first quadrant, confirming the geometry.