How do you draw a straight line in Python?

You can plot points using the equation y = mx + c and use the Canvas API's moveTo() and lineTo() methods to draw the line.

What is the slope-intercept form in Python?

The slope-intercept form y = mx + c can be implemented in Python by varying x values and calculating corresponding y values.

Can you animate a moving point along a line?

Yes. By incrementing x and recalculating y, you can move a point smoothly along the linear path using requestAnimationFrame or setInterval.

Drawing and Animating along a Straight Line in Python

Understanding the Straight Line Equation in Python

In this tutorial, you'll learn how to draw and animate a straight line in Python using the slope-intercept form of a line. We'll explore how to calculate the equation of a straight line, plot it on a 2D coordinate plane, and even animate a point moving along the line using Python's graphics tools such as Turtle. Whether you're studying coordinate geometry or working on a Python graphics project, this guide will help you understand linear motion in a clear, visual way.

In coordinate geometry, whether for use in Python or any other language, the equation of a straight line has the general form y = mx + c;
where m is the slope and c is the intercept on the y-axis.

For a vertical line, x is constant and for a horizontal line, y is constant.
This formula helps in calculating and drawing straight lines in Python, whether for graphics, animations, or math-based programming.

Example: Finding the Line Equation Between Two Points | Maths Explanation for Python Kids

In Python, you can formulate line equation using two known points:
Given any 2 points on the Python Canvas (x₁, y₁) and (x₂, y₂); we'll have:

Figure: Python straight line graph coordinates for linear equation y = mx + c

	y₂ - y₁	=	y - y₁
	x₂ - x₁		x - x₁
⇒ y = (	y₂ - y₁	) x +	x₂y₁ - x₁y₂
	x₂ - x₁		x₂ - x₁

Comparing this linear equation, for the given Python canvas points, to the general equation of a straight line, i.e. y = mx + c

m =	y₂ - y₁
m =	x₂ - x₁
&
c =	x₂y₁ - x₁y₂
c =	x₂ - x₁

Say we are to find the equation for the line passing through the arbitrary points (50, 50) and (200, 100) on a Python canvas:

m =	100 - 50	=	50	=	1
	200 - 50		150		3
&
c =	200(50) - 50(100)		=	10000 - 5000
	200 - 50			150
=		5000	=		100
		150			3

Hence,
y = ¹/₃x + ¹⁰⁰/₃
or
3y = x + 100

This gives a Python-ready straight line equation that you can use to animate objects or draw lines on a canvas.

Python Code Example - Animate Object Along a Straight Line

To animate a dot along a straight line in Python, we can increment the x-coordinate and compute the matching y-coordinate using the equation of the line.

Let's do so with the above equation representing points (x₁, y₁) = (50, 50) and (x₂, y₂) = (100, 200).

Create 2 new Python files; File, New File.
Call them Facet.py and StraightLine.py.
Type out the adjoining Python / Turtle code for animating an image body through the path of a straight line.

Important: When trying to click on the button to get things started, you might need to click away from the button text.

Summary: Visualizing Linear Equations in Python

The straight line equation is one of the first concepts students learn in senior secondary mathematics. In Python, we can easily plot a line by defining its slope (m) and intercept (c). This Python maths tutorial demonstrates how to compute the equation of a line given two points and visualize it using code.

Using Python to draw straight lines helps students understand the relationship between slope and intercept in linear equations. We've learnt how to draw a straight line in Python using the equation y = mx + c. This lesson explained how to calculate slope and intercept, plot the straight line equation in Python, and even animate a moving dot along the line using Python's Turtle library.
This foundation helps you transition into more advanced Python graphics and animation projects.

So! Python Fun Practice Exercise - Animate in Straight Line

As a fun practice exercise, try modifying the Python code to explore different gradients and intercepts. This will be a great way to connect mathematics and programming, and help you understand more about Python animations and linear equations.

Python Straight Line Code for Turtle Template - Facet Class

import turtle

class Template:
    def __init__(self):
        screen = turtle.getscreen()
        screen.title("usingMaths.com")
        screen.setup(width=0.9, height=0.9, startx=None, starty=None)
        screen.colormode(255)
        self.bgcolour = "#cccccc"
        screen.bgcolor(self.bgcolour)
        screen.delay(0)
        self.screen = screen

        self.wnd_width = self.screen.window_width()
        self.wnd_height = self.screen.window_height()

    def controlButtons(self):
        self.button = turtle.clone()

        turtle.speed(0)
        turtle.penup()
        turtle.setposition(-self.wnd_width/2, self.wnd_height/2)
        turtle.color("black", "pink")

        turtle.pendown()
        # draw button region
        turtle.begin_fill()
        turtle.forward(self.wnd_width)
        turtle.right(90)
        turtle.forward(50)
        turtle.right(90)
        turtle.forward(self.wnd_width)
        turtle.right(90)
        turtle.forward(50)
        turtle.end_fill()

        self.button.speed(0)
        self.button.penup()
        # draw button
        self.button.setposition(0, self.wnd_height/2 - 25)
        self.button.shape("square")
        self.button.resizemode("user")
        self.button.shapesize(2, 8)
        self.button.color("black", (255, 0, 255))

        return turtle.getturtle()

Python Animation Code for Straight Line class

#!usr/bin/env python3

from Facet import Template

def prep():
    global x1, y1, x_dot, y_dot, m, c, restart
    restart = False

    # bind fun function
    scene.button.onrelease(play)
    screen.delay(20)

    turtle.penup()
    # button text
    turtle.setposition(scene.button.xcor(), scene.button.ycor()-10)
    turtle.pendown()
    turtle.write("Move", align="center", font=("Arial",16,"bold"))

    # dot parameters
    diameter = 1
    dot_colour = "#ffff00"
    x1 = 30 - scene.wnd_width/2; y1 = scene.wnd_height/3
    x2 = scene.wnd_width/2 - 30; y2 = -scene.wnd_height/3
    x_dot = x1; y_dot = y1

    m = (y2 - y1) / (x2 - x1)
    c = (x2*y1 - x1*y2) / (x2 - x1)

    # transform turtle into a dot
    turtle.penup()
    turtle.setposition(x_dot, y_dot)
    turtle.setheading(0)
    turtle.shape("classic")
    turtle.shapesize(diameter, diameter)
    turtle.color(dot_colour, dot_colour)

# fun function when button is clicked
# just moves turtle until it hits the right boundary
def play(x, y):
    global x_dot, y_dot, m, c, x1, y1, restart

    if restart:
        turtle.clearstamps()
        restart = False

    if x_dot < scene.wnd_width/2 - 10*turtle.shapesize()[1]:
        y_dot = m*x_dot + c
        # change dot's coordinates
        turtle.setposition(x_dot, y_dot)
        turtle.stamp()

        x_dot += 20
        screen.ontimer(play(0,0), 500)
    else:
        x_dot = x1; y_dot = y1
        restart = True
        screen.mainloop()

# Let fly
scene = Template();
turtle = scene.controlButtons()
screen = scene.screen

prep()

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