Three-Dimensional Coordinate System There are a couple standard ways to graph points in three dimensions. The method this book uses is with the positive x-axis coming diagonally down to the left, the positive y-axis going diagonally down to the right, and the positive z-axis going up.
axis: The axis is the vertical line in the Cartesian coordinate system. It runs from bottom to top, and it represents the vertical position of points. The yaxis is labeled with numbers that increase as you move upward and decrease as you move downward.
The horizontal axis is usually called the x-axis. The vertical axis is usually called the y-axis. The point where the x- and y-axis intersect is called the origin.
X and y coordinates (axis) are horizontal and vertical addresses in a 2D space. The order of the x and y coordinates in the ordered pair is important. The x coordinate always comes first, followed by the y coordinate. That is why (3, 4) is not the same as (4, 3).
The order in which you write x- and y-coordinates in an ordered pair is very important. The x-coordinate always comes first, followed by the y-coordinate. As you can see in the coordinate grid below, the ordered pairs (3,4) and (4,3) are two different points!
The x axis is in the plane of the screen and is positive toward the right and negative toward the left. The y axis is in the plane of the screen and is positive toward the top and negative toward the bottom. The z axis is perpendicular to the screen or keyboard, and is positive extending outward from the screen.
The y-axis is a vertical number line and goes up and down.
A graph has two axes that form an L-shape. The axes are labelled 𝒙 and 𝒚. The 𝒙-axis is the horizontal line and the 𝒚-axis is the vertical line.