Intersection between draggable line and Plot Matplotlib on my GUI

I have a plot and a draggable line on it. I want to mark the intersection of the line and the plot when idle and also when moved, the intersection can be any marker.

Code for the draggable line:

class draggable_lines:
    def __init__(self, ax, kind, XorY):
        self.ax = ax
        self.c = ax.get_figure().canvas
        self.o = kind
        self.XorY = XorY

        if kind == "h":
            x = [-1, 1]
            y = [XorY, XorY]

        elif kind == "v":
            x = [XorY, XorY]
            y = [0, 5000000]
        self.line = lines.Line2D(x, y, picker=5)
        self.ax.add_line(self.line)
        self.c.draw_idle()
        self.sid = self.c.mpl_connect('pick_event', self.clickonline)

    def clickonline(self, event):
        if event.artist == self.line:
            print("line selected ", event.artist)
            self.follower = self.c.mpl_connect("motion_notify_event", self.followmouse)
            self.releaser = self.c.mpl_connect("button_press_event", self.releaseonclick)

    def followmouse(self, event):
        if self.o == "h":
            self.line.set_ydata([event.ydata, event.ydata])
        else:
            self.line.set_xdata([event.xdata, event.xdata])
        self.c.draw_idle()

    def releaseonclick(self, event):
        if self.o == "h":
            self.XorY = self.line.get_ydata()[0]
        else:
            self.XorY = self.line.get_xdata()[0]

        print (self.XorY)

        self.c.mpl_disconnect(self.releaser)
        self.c.mpl_disconnect(self.follower)

And code for plot for the GUI

        figure = Figure(figsize=(5, 4), dpi=100)
        plot = figure.add_subplot(1, 1, 1)
        figure.suptitle("Date", fontsize=12)
        Line, = plot.plot(x, y, color="Blue",linewidth = LineWidth)                                
        canvas = FigureCanvasTkAgg(figure, root)
        canvas.get_tk_widget().place(x=10,y=200)

        
        toolbar = NavigationToolbar2Tk(canvas, root, pack_toolbar=False)
        toolbar.update()
        toolbar.place(x=10,y=600)