The graphs of the lines x + 2y - 3 = 0 and 2x + 4y + 11 = 0 are:

For two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, the relationship between them is decided by comparing the ratios of corresponding coefficients:

• If a1/a2 is not equal to b1/b2, the lines intersect at exactly one point (a unique solution).

• If a1/a2 = b1/b2, and this is not equal to c1/c2, the lines are parallel and never meet (no solution).

• If a1/a2 = b1/b2 = c1/c2, the lines coincide (infinitely many solutions).

Apply this rule to the given lines:

1. Write down the coefficients: for x + 2y - 3 = 0, a1 = 1, b1 = 2, c1 = -3; for 2x + 4y + 11 = 0, a2 = 2, b2 = 4, c2 = 11.

2. Compute the coefficient ratios: a1/a2 = 1/2, b1/b2 = 2/4 = 1/2, and c1/c2 = -3/11.

3. Compare them: a1/a2 = b1/b2 = 1/2, but c1/c2 = -3/11, which is not equal to 1/2 - so the coefficient condition for parallel lines is satisfied.

Cross-check using the slope form (y = mx + c): x + 2y - 3 = 0 gives y = -x/2 + 3/2, slope = -1/2; 2x + 4y + 11 = 0 gives y = -x/2 - 11/4, slope = -1/2. Both lines have the same slope but different y-intercepts (3/2 and -11/4), confirming they never meet.

Hence, the two lines are parallel to each other.