Take a line passing through a point [tex](x_0,y_0)[/tex] with slope [tex]m[/tex].
Its point-slope form is
[tex]y-y_0=m(x-x_0)[/tex]
Its slope-intercept form is obtained by expanding and solving for [tex]y[/tex].
[tex]y=mx-mx_0+y_0[/tex]
and [tex]-mx_0+y_0[/tex] is the intercept on the y-axis.
By "genera form", I assume you mean its standard form, which is obtained by moving all terms with [tex]x[/tex] and [tex]y[/tex] to one side and setting it equal to a constant.
[tex]y-mx=-mx_0+y_0[/tex]
