The graphic representation of the equations x + 2y = 3 and 2x + 4y + 7 = 0 gives a pair of

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Parallel lines Explanation: 1. Express standard forms Convert both linear equations into the standard form aix + biy + ci = 0: Equation 1TgQPHd||[]: x + 2y – 3 = 0 Here, a1 = 1, b1 = 2 and c1 = –3. Equation 2TgQPHd||[]: 2x + 4y + 7 = 0 Here, a2 = 2, b2 = 4 and c2 = 7. 2. Compare the coefficients We find the ratios of the coefficients of x, y and the constant terms: (a_1)/(a_2) = $\frac{1}{2}$ (b_1)/(b_2) = $\frac{2}{4}$ = $\frac{1}{2}$ (c_1)/(c_2) = (-3)/7 Since `(a_1)/(a_2) = (b_1)/(b_2) $\neq$ (c_1)/(c_2)`, the given lines have the same slope but different intercepts. This satisfies the condition for a pair of parallel lines. [Solution diagram: 467936_solution_1.png]

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