A line cuts off intercept \(p\) on the \(x\)-axis and intercept \(q\) on the \(y\)-axis, where \(p > q\). The sum of the intercepts is \(2\) and the product of the intercepts is \(-15\). What is the equation of the line?
\(3x-5y-15=0\)
The intercepts \(p\) and \(q\) satisfy \(p+q=2\) and \(pq=-15\), so they are roots of \(t^2-2t-15=0\), giving \(t=5\) or \(t=-3\). Since \(p>q\), \(p=5,\ q=-3\). The intercept form \(\dfrac{x}{5}+\dfrac{y}{-3}=1\) simplifies to \(3x-5y-15=0\).
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