The y-intercept of the line given by the equation in the question can be obtained by simply substituting the value of x with 0 and then solving for the corresonding value of y, as follows:
[tex]\begin{gathered} 6x-y=1 \\ \text{when x =0:} \\ \Rightarrow6(0)-y=1 \\ \Rightarrow0-y=1 \\ \Rightarrow-y=1 \\ \Rightarrow y=-1 \end{gathered}[/tex]