1. The problem is to identify and understand the numbered quadrants of a graph used for plotting linear equations. 2. The Cartesian coordinate plane is divided into four quadrants by the x-axis (horizontal) and y-axis (vertical). 3. The quadrants are numbered counterclockwise starting from the upper right: - Quadrant I: $x > 0$, $y > 0$ - Quadrant II: $x < 0$, $y > 0$ - Quadrant III: $x < 0$, $y < 0$ - Quadrant IV: $x > 0$, $y < 0$ 4. When graphing linear equations, the line may pass through one or more of these quadrants depending on its slope and intercept. 5. Understanding which quadrant a point lies in helps analyze the behavior of the linear equation. 6. For example, the line $y = mx + b$ can be plotted and its intercepts with axes determine which quadrants it crosses. 7. This knowledge is fundamental for graphing and interpreting linear equations in algebra.