In this Grade 7 lesson from Yoshiwara Intermediate Algebra, students learn how to represent real-world relationships using three mathematical tools: tables of values, graphs, and algebraic equations. The lesson introduces the concept of a linear model through practical examples, such as writing an equation for commission-based income and calculating bike rental costs using expressions like C = 5 + 3t. Students practice moving between all three representations to analyze data, identify trends, and make predictions from a linear relationship.
Section 1
📘 Linear Models
A linear model simplifies reality by describing a variable that changes at a constant rate. We'll represent these relationships with tables, graphs, and the equation .
Now, let's put this into practice. You'll work through interactive examples, building linear models using tables, graphs, and equations from word problems.
Section 2
Mathematical model
A mathematical model is a simplified description of reality that uses mathematics to help us understand a system or process. We can represent the relationship between variables by:
For a bike rental with a 5 dollar fee and 3 dollars per hour rate, the cost for time can be shown as a table: (0, 5), (1, 8), (2, 11).
Section 3
Linear model
A linear model describes a variable that increases or decreases at a constant rate. It has the form
April's income is 200 dollars per week plus 9% commission on sales . Her income is .
Section 4
Evaluating expressions vs. solving equations
For an equation like :
To find the cost of a 6-hour bike rental using , you evaluate: dollars.
Section 5
Decreasing linear models
A decreasing linear model describes a quantity that reduces at a constant rate. The rate is subtracted from the starting value. For a starting value of 20 and a rate of per mile , the equation is:
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Section 1
📘 Linear Models
A linear model simplifies reality by describing a variable that changes at a constant rate. We'll represent these relationships with tables, graphs, and the equation .
Now, let's put this into practice. You'll work through interactive examples, building linear models using tables, graphs, and equations from word problems.
Section 2
Mathematical model
A mathematical model is a simplified description of reality that uses mathematics to help us understand a system or process. We can represent the relationship between variables by:
For a bike rental with a 5 dollar fee and 3 dollars per hour rate, the cost for time can be shown as a table: (0, 5), (1, 8), (2, 11).
Section 3
Linear model
A linear model describes a variable that increases or decreases at a constant rate. It has the form
April's income is 200 dollars per week plus 9% commission on sales . Her income is .
Section 4
Evaluating expressions vs. solving equations
For an equation like :
To find the cost of a 6-hour bike rental using , you evaluate: dollars.
Section 5
Decreasing linear models
A decreasing linear model describes a quantity that reduces at a constant rate. The rate is subtracted from the starting value. For a starting value of 20 and a rate of per mile , the equation is:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter