In this graph is the slope of the dotted line the transistor

In this graph, is the slope of the dotted line the transistor gain and the point where all the solid lines meet (base of the dotted line) the value of V_t?

Solution

Yes.

As you said, the point where the the dotted lines (black lines) and the solid lines meet, is the value of Vt, and it is constant.

However, this intersection point depends on the Vgs value, that will affect the Vds value.

Taking in account that the Vgs value has to be greater than the threshold voltage, Vt, so that the transistor works.