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Linear Relations

The topic of Linear Relations is an important foundation for understanding functions and relations in higher level mathematics. 


When first introduced to linear relations, students can investigate linear growing patterns and represent them using concrete 

materials, graphs and algebraic expressions. As students build their understanding, they should begin to describe the characteristics of linear relations and be able to connect the various representations (graph, table and equation). As well, they should understand the role of slope and y-intercept in determining the direction and starting point of a line (including negative slopes). To further consolidate understanding, students can explore how to determine the equation of a line using algebraic methods and investigate horizontal and vertical lines.

While Linear Relations are important in math, Line is also one of the key Elements of Design

Students can use both organic and geometric line in their artworks. Lines can be continuous, implied or broken.

To access any lesson below, click on the image of the file in the right column. 


Students need to review how to plot coordinate points in order to investigate the graphs of linear relations. 

Link to lesson.


Linear Patterns & Nature

Students will gain an understanding of how to create a linear pattern using items found in nature. They will be asked to represent their pattern as a graph, table and equation.

Link to lesson.


Linear Patterns & Colour Theory

Learn the basics of colour theory while investigating the various representations of linear patterns (visual, table, graph and equation).

Link to lesson.


Linear Patterns & Painting Techniques

An introduction to different painting techniques and a continuation of investigating linear patterns. 

Extension includes looking at decreasing patterns.

Link to lesson.


Create Your Own Linear Pattern

Use the template provided to create your own linear pattern. Share your design with us through Twitter, Facebook or Instagram using the handle @artofmathed.

Link to lesson.


Equations of Lines

Learn how to determine the equation of a line in slope y-intercept form (y = mx + b). Includes practice questions with solutions.

Create your own artwork using the element of Line and upload your image to Desmos. Find the coordinates of two points on one of the lines and use these points to determine the equation. 

Link to lesson.


How to Upload an Image to Desmos

Desmos is an online graphing program that allows images to be uploaded as a background in a graph. 

Take a photo of an image containing lines. Upload the image to Desmos and find two points on a line. Use those points to determine the equation of your line. 

Share your design with us through Twitter, Facebook or Instagram using the handle @artofmathed.

Link to handout.



Learn how to use one and two point perspective to add depth to an image.  Learn about the Parthenon in Greece.  Create your own art history video or podcast, answer the 5 Ws (who?what?where?when?why?) and share with @ArtofMathEd

Use the vanishing point on a graph to investigate the point of intersection of a system of linear equations. Use this Desmos link and add lines through the points provided. Can you add any more? Share a screenshot with @ArtofMathEd

Link to lesson.


Perspective, Slope & Line

Learn About Perspective Drawing, Slope & Equations of Lines through the art of Kazuo Nakamura. 


Art Canada Institute Educator's Resource 

Supporting Videos


Investigating Trends

Use the mass and volume of soapstone sculptures to investigate the density of soapstone.

Create your own sculpture using an available medium (soapstone, clay, play dough etc). Share your project using Twitter, Instagram or Facebook and tag us using the handle @ArtofMathEd

Link to handout.

The Coordinate Plane
Linear Patterns & Outdoor Ed
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Create Your Own Linear Pattern.png
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Investigating Density
Investigating Trends
Slope & Line
Perspective Lesson
Equatins of Lines
Create Your Own
Colour Theory
Plotting Coordinate Points
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