Exploring Algebraic Relationships through Tables

This video tutorial introduces algebraic relationships using variables, independent and dependent quantities. It explains how to use tables to represent these relationships and solve problems by identifying input and output values. The tutorial also covers working backwards to find independent quantities and using visual models to understand input-output relationships. Finally, it demonstrates how to graph data from tables, emphasizing the importance of labeling axes and plotting ordered pairs.

What is a variable in algebra?

• A mathematical operation

• A symbol representing an unknown number

• A type of equation

• A fixed number

What do we call the input value in a table?

• Dependent variable

• Constant

• Output value

• Independent variable

If the rule is x + 8 and the input is 10, what is the output?

• 18

• 20

• 8

• 10

For the rule 5 * x, what is the output if the input is 4?

• 9

• 20

• 5

• 4

How do you find the input if the output is found by multiplying by 2?

• Divide by 2

• Add 2

• Multiply by 2

• Subtract 2

If the output is 14 and the rule is 2 * x, what is the input?

• 2

• 14

• 28

• 7

In a model with 2 gray squares and 4 white squares, what is the total number of squares?

• 2

• 4

• 6

• 8

For the rule 2 + x * 2, what is the output if the input is 3?

• 10

• 8

• 6

• 5

What should you label the x-axis when graphing input values?

• Independent

• Dependent

• Variable

• Output

Why do we not graph the ordered pair (10, 22) in the final graph?

• It is not part of the data

• It does not fit on the graph

• It is incorrect

• It is not an ordered pair