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For the lines \(y=mx+c\) and \(y=mx+d\), where \(c\ne d\), which statement about their relationship is correct?रेखाएँ \(y=mx+c\) और \(y=mx+d\) में \(c\ne d\) हो, तो इन दोनों रेखाओं के संबंध के बारे में कौन-सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: They are distinct parallel linesवे अलग-अलग समानांतर रेखाएँ हैं
Both lines have the same slope \(m\), so they have the same direction. Since \(c\ne d\), their y-intercepts differ; therefore, they are not coincident but distinct parallel lines. Exam tip: same slope with different y-intercepts means parallel lines.दोनों रेखाओं की ढाल \(m\) समान है, इसलिए उनकी दिशाएँ समान हैं। चूँकि \(c\ne d\), उनके y-अवरोध अलग हैं; अतः वे संपाती नहीं, अलग-अलग समानांतर रेखाएँ हैं। परीक्षा टिप: समान ढाल और अलग y-अवरोध = समानांतर रेखाएँ।
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