X and y axis

The x-axis and y-axis are axes in the Cartesian coordinate system. Together, they form a coordinate plane. The x-axis is usually the horizontal axis, while the y-axis is the vertical axis. They are represented by two number lines that intersect perpendicularly at the origin, located at (0, 0), as shown in the figure below.

Specifying a point on the x- and y-axis

You can specify a point using an ordered pair of numbers, (x, y). The first number in the pair corresponds to a number on the x-axis and the second number corresponds to a number on the y-axis. The numbers in the ordered pair are called the x-coordinate and the y-coordinate of the point.

Points A, B, and C are graphed on the coordinate plane above. Starting from the origin, follow the steps below to find the real number for each coordinate in the ordered pair.

  1. For point A, move to the right 3 units on the x-axis to get an x-coordinate of 3, then move up 4 units on the y-axis to get a y-coordinate of 4.
  2. For point B, move to the left 4 units on the x-axis to get an x-coordinate of -4. Since there is no vertical distance to move on the y-axis the y-coordinate is 0.
  3. For point C, move to the right 4 units on the x-axis to get an x-coordinate of 4, then move down 4 units on the y-axis to get a y-coordinate of -4.

x- and y-intercepts

The x-intercept is a point at which a graph intercepts the x-axis. Likewise, the y-intercept is a point at which a graph intercepts the y-axis. The y-coordinate of an x-intercept is always 0, and the x-coordinate of a y-intercept is always 0.

Given an equation, plugging in x = 0 will yield the y-intercept and plugging in y = 0 will yield the x-intercept.

Example:

Find the coordinates of the x- and y-intercepts of the graph of y = 2x + 6.

Plug y = 0 into y = 2x + 6:

0 = 2x + 6

-6 = 2x

x = -3

The x-intercept is located at (-3, 0).

Plug x = 0 into the equation:

y = 2 × 0 + 6

y = 6

The y-intercept is located at (0, 6).