How to show a line being drawn from one point to another?

You can use an AnimationController to control the animation duration.

To draw the line “step by step” you can use a Tween (linear interpolation between a beginning and ending value).

Then you just need to pass the current progress to your line painter and calculate the new width/height on each paint() when you call canvas.drawLine.

Working example :

import 'package:flutter/material.dart';

class Line extends StatefulWidget {
  @override
  State<StatefulWidget> createState() => _LineState();
}

class _LineState extends State<Line> with SingleTickerProviderStateMixin {
  double _progress = 0.0;
  Animation<double> animation;

  @override
  void initState() {
    super.initState();
    var controller = AnimationController(duration: Duration(milliseconds: 3000), vsync: this);

    animation = Tween(begin: 1.0, end: 0.0).animate(controller)
      ..addListener(() {
        setState(() {
          _progress = animation.value;
        });
      });

    controller.forward();
  }

  @override
  Widget build(BuildContext context) {
    return CustomPaint(painter: LinePainter(_progress));
  }
}

class LinePainter extends CustomPainter {
  Paint _paint;
  double _progress;

  LinePainter(this._progress) {
    _paint = Paint()
      ..color = Colors.green
      ..strokeWidth = 8.0;
  }

  @override
  void paint(Canvas canvas, Size size) {
    canvas.drawLine(Offset(0.0, 0.0), Offset(size.width - size.width * _progress, size.height - size.height * _progress), _paint);
  }

  @override
  bool shouldRepaint(LinePainter oldDelegate) {
    return oldDelegate._progress != _progress;
  }
}

Then use it like this :

import 'package:flutter/material.dart';

class Home extends StatefulWidget {
  @override
  State<StatefulWidget> createState() {
    return _HomeState();
  }
}

class _HomeState extends State<Home> {
  Widget build(BuildContext context) {
    return new Scaffold(
      appBar: AppBar(
        title: Text('Line animation'),
        leading: new Icon(Icons.insert_emoticon),
      ),
      backgroundColor: Colors.white,
      body: SizedBox(height: 200, width: 200, child: Line()),
    );
  }
}

The line will be drawn in the sized box from 0,0 to 200,200 in 3 seconds.

Result :