Pieces of a Mystery Line

Geometry Level 2

Consider two lines \[9x+4y+1=0, \hspace{.5cm} 4x+15y+16=0.\] If a third line \(y=mx+b\) has the same slope as the first line and passes through the \(x\)-intercept of the second line, what is \(\frac{b}{m}\)?

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