Class 11 Mathematics - Straight Lines - Various forms of the equation of a line Easy Quiz

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रेखा \(y=-3x+5\) का \(y\)-अक्ष प्रतिच्छेद क्या है?

What is the \(y\)-intercept of the line \(y=-3x+5\)?

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Correct Answer

A. 5

Explanation

Simple Explanation

रेखा के मानक रूप \(y=mx+c\) में \(y\)-अक्ष प्रतिच्छेद \(c\) होता है, क्योंकि \(x=0\) रखने पर \(y=c\) मिलता है। यहाँ \(c=5\), इसलिए \(y\)-अक्ष प्रतिच्छेद 5 है और बिंदु \((0,5)\) होगा। विकल्प \(-3\) ढाल है, प्रतिच्छेद नहीं। परीक्षा-टिप: \(y\)-अक्ष पर स्थित बिंदु के लिए हमेशा \(x=0\) रखें। / In the standard form \(y=mx+c\), the \(y\)-intercept is \(c\), since putting \(x=0\) gives \(y=c\). Here, \(c=5\), so the \(y\)-intercept is 5 and the point is \((0,5)\). The value \(-3\) is the slope, not the intercept. Exam tip: For any point on the \(y\)-axis, substitute \(x=0\).

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समीकरण \(x=-2\) का ग्राफ किस प्रकार की रेखा है?

What type of line is represented by the equation \(x=-2\)?

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Correct Answer

B. लंबवत रेखाVertical line

Explanation

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समीकरण \(x=-2\) में \(x\) का मान हर बिंदु पर निश्चित रहता है, जबकि \(y\) का मान कोई भी हो सकता है। इसलिए इसके सभी बिंदु \((-2,y)\) के रूप में होंगे और यह \(y\)-अक्ष के समानांतर एक लंबवत रेखा होगी। क्षैतिज रेखा के लिए समीकरण \(y=\text{स्थिरांक}\) होता है। परीक्षा में याद रखें: \(x=\text{स्थिरांक}\) लंबवत रेखा और \(y=\text{स्थिरांक}\) क्षैतिज रेखा दर्शाता है। / In the equation \(x=-2\), the value of \(x\) remains fixed at , while \(y\) can take any value. Thus, all points are of the form \((-2,y)\), forming a vertical line parallel to the \(y\)-axis. A horizontal line has the form \(y=\text{constant}\). Exam tip: \(x=\text{constant}\) represents a vertical line, whereas \(y=\text{constant}\) represents a horizontal line.

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