Touchy Circles

Geometry Level 2

Circles \(A\) and \(B\) are placed in the first quadrant so that circle \(A\) is tangent to both the \(x\)-axis and the \(y\)-axis while circle \(B\) is tangent to the \(x\)-axis and is externally tangent to circle \(A\).

If the radius of circle \(B\) is half the radius of circle \(A\), then what is the slope of the line passing through the centers of \(A\) and \(B\)?

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