Take a line passing through a point \((x_0,y_0)\) with slope \(m\).
Its point-slope form is
\(y-y_0=m(x-x_0)\)
Its slope-intercept form is obtained by expanding and solving for \(y\).
\(y=mx-mx_0+y_0\)
and \(-mx_0+y_0\) 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 \(x\) and \(y\) to one side and setting it equal to a constant.
\(y-mx=-mx_0+y_0\)
