1. The problem is to understand how to graph points on the Cartesian plane and interpret their positions. 2. The Cartesian plane consists of two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical). 3. Each point on the plane is represented as an ordered pair $(x,y)$, where $x$ is the horizontal coordinate and $y$ is the vertical coordinate. 4. To graph a point, start at the origin $(0,0)$, move $x$ units along the x-axis (right if positive, left if negative), then move $y$ units along the y-axis (up if positive, down if negative). 5. For example, to graph the point $(3, -2)$, move 3 units right and 2 units down from the origin. 6. The formula for distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ which helps understand spacing on the plane. 7. Important rules: the x-coordinate always comes first, and the y-coordinate second; points with the same x-value lie on a vertical line; points with the same y-value lie on a horizontal line. 8. Practice by plotting points such as $(0,0)$, $(4,5)$, $(-3,1)$, and $(-2,-4)$ to get comfortable with the Cartesian plane. 9. Understanding this foundation is essential for graphing equations and analyzing geometric relationships.