This lesson involves using the graphs of two lines to create equivalent expressions.

• Students will learn the distributive property of multiplication over addition for real numbers.
• Students will verify that algebraic expressions involving the distributive property are equivalent both graphically and algebraically.

• Distributive Property of Multiplication over Addition
• real numbers
• equivalent expressions
• coinciding lines

This lesson involves using the graphs of two lines to create equivalent expressions.
As a result, students will:

• Change the values of a and b in the second line until the graphs coincide and explain why this shows that they now have equivalent expressions.
• Generate several other examples and derive a rule for generating equivalent algebraic expressions using the distributive rule, i.e. a(x + c) = ax + ac.
• Change the values of a and c so that the graph a(x + c)matches the graph of one of the form ax + b.
• Generate several other examples and derive a rule for generating equivalent algebraic expressions using the distributive rule in reverse, i.e. ax + ac = a(x + c).