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.
- 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.
- 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.
- 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.
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).