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If the line (y=(k-3)x+2) increases (y) by (48) when (x) increases by (6), what is (k)?यदि रेखा (y=(k-3)x+2) (x) के (6) बढ़ने पर (y) (48) बढ़ाती है, तो (k) क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(11\)\(11\)
The slope of the line is \(k-3\). Since \(y\) increases by \(48\) when \(x\) increases by \(6\), the slope is \(\frac{48}{6}=8\). Thus, \(k-3=8\), so \(k=11\). If \(k=10\), the slope would be only \(7\), giving a rise of \(42\) for a run of \(6\). Exam tip: in \(y=mx+c\), \(m\) is the slope.रेखा का ढाल \(k-3\) है। यहाँ \(x\) में वृद्धि \(6\) और \(y\) में वृद्धि \(48\) है, इसलिए ढाल \(\frac{48}{6}=8\) होगी। अतः \(k-3=8\), जिससे \(k=11\) मिलता है। \(10\) लेने पर ढाल केवल \(7\) होगी, जो \(x\) में \(6\) की वृद्धि पर \(y\) को \(42\) ही बढ़ाएगी। परीक्षा टिप: रेखा \(y=mx+c\) में \(m\) हमेशा ढाल होता है।
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