Two lines are given to be parallel. The equation of one of these lines is $5x - 3y = 2$. The equation of the second line can be :
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer
Option D: $-15x + 9y = 5$
For parallel lines, $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$. Here $5x - 3y = 2$, so $a_1:b_1 = 5:(-3)$. Option D gives $-15x + 9y = 5$, where $\dfrac{5}{-15} = \dfrac{-3}{9} = -\dfrac{1}{3}$, but $\dfrac{-2}{-5} \neq -\dfrac{1}{3}$. ✓ Parallel condition satisfied.
Explanation
- For parallel lines: $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$.
- Check each option for the ratio of coefficients of $x$ and $y$ being equal (not $c$-ratio).
- Option D: ratios of $x$- and $y$-coefficients are both $-\frac{1}{3}$, but the constant ratio differs → parallel.
- Eliminate options: A has unequal $a/b$ ratios; B has unequal ratios; C has unequal ratios ($9/-15 \neq -15/6$).