In the coordinate plane \(p\ne 1,\) a line \(L\) passes through a point \((1,p).\) What is the slope of the line \(L?\)

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In the coordinate plane \(p\ne 1,\) a line \(L\) passes through a point \((1,p).\) What is the slope of the line \(L?\)

(1) The line \(L\) passes through the point \((0,1).\)
(2) The line \(L\) passes through point \((p,13).\)

Answer: E

Source: GMAT Club Tests