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Grades 9/10/11 Linear Relations and Analytic Geometry
Linear and non-linear relations. Solving linear equations and linear systems. Analytic geometry and statistics.
This is one of seven strands of the CEMC Grade 9/10/11 courseware. The other strands and more information about this courseware is available on the Grade 9/10/11 homepage.
Units
Unit 1: Linear Equations
Unit 2: Characteristics of Linear Relations
In this lesson, we will explore characteristics of a linear relationship between two variables using patterns, tables of values, and graphs. A variable is identified as being independent or dependent and comparisons are made between linear and non-linear relations.
In this lesson, we will continue to identify properties of a linear relation. We will define rate of change and initial value. We will then determine the rate of change and initial value from tables and graphs and use these values to develop a corresponding linear equation. In addition, we will calculate first differences in a table of values and use this to identify a relation as linear or non-linear.
In this lesson, we will define the terms direct variation and partial variation. We will use these definitions to identify which of the two variations a linear relationship represents.
In this lesson, we will introduce the terms slope and \(y\)-intercept. We will identify the slope and \(y\)-intercept in various representations of a linear relation. In addition, the idea of linear families will be explored.
In this lesson, we will look at various ways to graph linear relations by hand.
All of the pencil and paper practice exercises, answers, and solutions for this unit are reproduced here.
This is a collection of additional, and sometimes challenging, problems that extend the material covered in this unit, connect material from different lessons, and further explore real-world applications.