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Which line gives (y=15) at (x=0) and has slope (-3)?कौन सी रेखा (x=0) पर (y=15) देती है और ढाल (-3) रखती है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(y=-3x+15\)\(y=-3x+15\)
The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope and \(c\) is the y-intercept. Here, \(m=-3\), and \(y=15\) when \(x=0\), so \(c=15\). Therefore, the line is \(y=-3x+15\). Option A has y-intercept 15, but its slope is \(+3\), not \(-3\). Exam tip: In \(y=mx+c\), the coefficient of \(x\) is the slope.रेखा का ढाल-अवरोध रूप \(y=mx+c\) है, जहाँ \(m\) ढाल और \(c\) y-अवरोध है। यहाँ \(m=-3\) तथा \(x=0\) पर \(y=15\) है, इसलिए \(c=15\)। अतः रेखा \(y=-3x+15\) होगी। विकल्प A में y-अवरोध 15 है, लेकिन उसकी ढाल \(+3\) है, \(-3\) नहीं। परीक्षा टिप: \(y=mx+c\) में \(x\) का गुणांक हमेशा ढाल बताता है।
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