Lesson 4: Writing Equations in Two Variables

Property

In a relationship between two quantities, the independent variable is the quantity that is changed or controlled (the cause).
The dependent variable is the quantity that is measured or observed as a result (the effect).

Examples

Property

An equation in two variables shows the relationship between an independent variable (input) and a dependent variable (output).
These equations have the general form where one variable is expressed in terms of another, such as $y = mx + b$, $y = kx$, or other forms like $A = lw$. In these equations:

• One variable represents the input (independent variable)
• The other variable represents the output (dependent variable)
• Constants and coefficients determine how the variables relate to each other

Examples

Property

An equation in two variables, such as $y = 4x - 2$, has many solutions.
Each solution consists of an ordered pair of values, one for $x$ and one for $y$, that together satisfy the equation (make the equation true.)

Examples

The ordered pair $(1, 3)$ is not a solution of $y = 4x - 2$ because substituting the values gives $4(1) - 2 = 2$. Since the y-value is 3, and $3 \ne 2$, the pair is not a solution.