Multiple Representations

Front

What does the equation y = 13x represent in a real-world context?

Back

It represents a situation where a quantity y is directly proportional to x, with a constant of proportionality of 13. For example, if Vanessa buys x number of shirts for $13 each, then y (the total cost) equals 13 times x.

Front

What are independent quantities?

Back

Independent quantities are the variables that can be changed or controlled in an experiment or equation. They are often represented on the x-axis of a graph.

Front

What is the equation to represent the total weight of a backpack and an instrument?

Back

The equation is y = 10 + x, where y is the total weight, 10 is the weight of the backpack, and x is the weight of the instrument.

Front

What are dependent quantities?

Back

Dependent quantities are the variables that depend on the independent quantities. They are often represented on the y-axis of a graph.

Front

How do you identify a relationship in a table?

Back

You look for patterns or consistent changes in the values of the independent and dependent quantities.

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities increase or decrease at the same rate, often represented by the equation y = kx, where k is a constant.

Front

What does the term 'variable' mean in mathematics?

Back

A variable is a symbol used to represent an unknown value in an equation or expression.

Front

What is the difference between an equation and an expression?

Back

An equation states that two expressions are equal, while an expression is a combination of numbers, variables, and operations without an equality sign.

Front

What is the purpose of a graph in representing data?

Back

A graph visually represents the relationship between two or more quantities, making it easier to identify trends and patterns.

Front

What does it mean for a quantity to be 'dependent' on another?

Back

It means that the value of the dependent quantity changes in response to changes in the independent quantity.