diff --git a/Line.go b/Line.go
new file mode 100644
index 0000000..2955b2e
--- /dev/null
+++ b/Line.go
@@ -0,0 +1,44 @@
+package main
+
+import (
+	"fmt"
+	"log"
+	"math"
+)
+
+type line struct {
+	k float64
+	b float64
+}
+
+func (l *line) y(x float64) float64 {
+	return l.k*x + l.b
+}
+
+func NewLine() *line {
+	return &line{0, 0}
+}
+
+func (l *line) Train(points []point, lr float64, epochs uint) error {
+	for i := uint(0); i < epochs; i++ {
+		y := make([]float64, len(points))
+		for j := range points {
+			y[j] = l.y(points[j].x)
+		}
+
+		var sum1, sum2 float64
+		for j := range points {
+			sum1 += y[j] - points[j].y
+			sum2 += y[j] - points[j].y*points[j].x
+		}
+
+		l.k -= lr * (2 / float64(len(points))) * sum2
+		l.b -= lr * (2 / float64(len(points))) * sum1
+		loss := sum1 / float64(len(points))
+		if math.IsNaN(loss) || math.IsInf(loss, 0) {
+			return fmt.Errorf("training unsuccessful")
+		}
+		log.Printf("Epoch: %d/%d, Loss %f\n", i, epochs, loss)
+	}
+	return nil
+}
diff --git a/main.go b/main.go
index e39985b..92d5f2b 100644
--- a/main.go
+++ b/main.go
@@ -3,31 +3,53 @@ package main
 import (
 	"image"
 	"log"
-	"time"
 
 	"github.com/hajimehoshi/ebiten/v2"
 )
 
-func f(x float64) float64  { return x*x + 5*x - 3 }
-func df(x float64) float64 { return 2*x + 5 }
+const (
+	e = 1e-5
+)
+
+func f(x float64) float64 { return x*x*x*x + x*x + 5*x - 3 }
+
+func df(x float64) float64 { return 4*x*x*x + 2*x + 5 }
+
+// func Derivative(x float64, f func(x float64) float64) float64 {
+// 	return (f(x+e) - f(x)) / e
+// }
 
 func main() {
+	p := NewRandomPoints(10)
+	l := NewLine()
+	err := l.Train(p, 0.001, 5000)
+	if err != nil {
+		log.Fatal(err)
+	}
 	ebiten.SetWindowSize(640, 480)
 	ebiten.SetWindowTitle("Gradient descent")
 
 	img := make(chan *image.RGBA, 1)
 	go func() {
-		p := Plot(-5, 0, 0.1, f)
-		x := 0.0
-		img <- p(x)
-		for i := 0; i < 50; i++ {
-			time.Sleep(30 * time.Millisecond)
-			x -= df(x) * 0.1
-			img <- p(x)
+		p := Plot(-30, 30, 0.1, f)
+		x := 30.0
+		img <- p(x, false)
+		for i := 0; i < 500000; i++ {
+			// time.Sleep( * time.Millisecond)
+			x -= df(x) * 1e-6
+			img <- p(x, false)
 		}
+
 	}()
 
 	if err := ebiten.RunGame(&App{Img: img}); err != nil {
 		log.Fatal(err)
 	}
 }
+
+func Abs(a float64) float64 {
+	if a < 0 {
+		return a * -1
+	}
+	return a
+}
diff --git a/plot.go b/plot.go
index ebad8a9..b6eae71 100644
--- a/plot.go
+++ b/plot.go
@@ -13,7 +13,7 @@ import (
 	"gonum.org/v1/plot/vg/vgimg"
 )
 
-func Plot(xmin, xmax, xstep float64, f func(float64) float64) func(x float64) *image.RGBA {
+func Plot(xmin, xmax, xstep float64, f func(float64) float64) func(x float64, isMinimum bool) *image.RGBA {
 	var pts plotter.XYs
 	for x := xmin; x <= xmax; x += xstep {
 		pts = append(pts, plotter.XY{X: x, Y: f(x)})
@@ -23,17 +23,23 @@ func Plot(xmin, xmax, xstep float64, f func(float64) float64) func(x float64) *i
 		log.Fatalf("Failed to NewLine: %v", err)
 	}
 	fn.Color = color.RGBA{B: 255, A: 255}
-	return func(x float64) *image.RGBA {
+	return func(x float64, isMinimum bool) *image.RGBA {
 		pts := plotter.XYs{{X: x, Y: f(x)}}
 		xScatter, err := plotter.NewScatter(pts)
 		if err != nil {
 			log.Fatalf("Failed to NewScatter: %v", err)
 		}
-		xScatter.Color = color.RGBA{R: 255, A: 255}
+		if isMinimum {
+			xScatter.Color = color.RGBA{G: 255, A: 255}
+
+		} else {
+			xScatter.Color = color.RGBA{R: 255, A: 255}
+
+		}
 
 		labels, err := plotter.NewLabels(plotter.XYLabels{
 			XYs:    pts,
-			Labels: []string{fmt.Sprintf("x = %.2f", x)},
+			Labels: []string{fmt.Sprintf("x = %.5f", x)},
 		})
 		labels.Offset = vg.Point{X: -10, Y: 15}
 		if err != nil {
diff --git a/point.go b/point.go
new file mode 100644
index 0000000..b934459
--- /dev/null
+++ b/point.go
@@ -0,0 +1,15 @@
+package main
+
+import "math/rand"
+
+type point struct {
+	x, y float64
+}
+
+func NewRandomPoints(num int) []point {
+	points := make([]point, num)
+	for i := 0; i < num; i++ {
+		points[i] = point{rand.Float64() * 300, rand.Float64() * 300}
+	}
+	return points
+}