91Ó°ÊÓ

Pre-Algebra acts as the foundation for understanding algebraic concepts like equations and functions. It typically includes operations on numbers, the understanding of variables, and grasping simple equations.
- Variables are symbols that stand for unknown numbers, usually represented by letters like "x" or "y".
- An equation is a statement of equality between two expressions. For instance, in the equation \( y = -4x \), "y" and "x" are variables connected by an equality sign.
- Operations like addition, subtraction, multiplication, and division are used to solve these equations.
In pre-algebra, the focus is on interpreting mathematical relationships and basic equation solving. Understanding these concepts is crucial for working with linear equations like \( y = -4x \), as you'll use the operations described to find the values you need.

The coordinate system is a method for visually representing equations, and it's often used to plot data points that depict mathematical relationships.
- It consists of two perpendicular lines: the horizontal line, called the x-axis, and the vertical line, called the y-axis.
- Each point in this system is determined by an ordered pair \((x, y)\).
- The x-value shows the position along the horizontal axis, while the y-value shows the position along the vertical axis.
Using the equation \( y = -4x \), you can determine points and plot them on this system. For instance, when \( x = -2 \), \( y = 8 \), creating the point \((-2, 8)\). By plotting all calculated pairs from the function, a straight line will be formed, showcasing the linear relationship as a visual line graph.

Function tables are useful tools for organizing and understanding the relationships between variables in an equation. Here's how they work:
- A function table lists input values, in this case, values of \( x \), and calculates the corresponding \( y \) values using a set equation.
- The relationship observed in the table is defined by the equation rule for converting \( x \) inputs to \( y \) outputs, such as \( y = -4x \).
- You simply follow this rule for each value of \( x \) to determine the corresponding \( y \). For instance, when \( x = -1 \), substituting into the equation gives \( y = 4 \).
Tables not only help in solving the equation but also reveal patterns, enabling prediction of outputs for uncalculated inputs. Filling in function tables with calculated \( y \) values for provided \( x \) inputs solidifies this understanding and visually represents the function's consistency and behavior.