interceptos

Interceptos, in mathematics, are the points where a graph or geometric object intersects a coordinate axis or plane. In two dimensions, the most common interceptos are the x-intercepts (points where the graph meets the x-axis) and the y-intercepts (points where the graph meets the y-axis). In three dimensions, a graph or surface can have interceptos with the x-, y-, and z-axes.

For a function y = f(x), the y-intercept is the value of f(0), giving the point (0, f(0)). The x-intercept(s) are the solutions to f(x) = 0, giving points (x, 0). A line in slope-intercept form, y = mx + b, has a y-intercept at (0, b) and an x-intercept at (-b/m, 0) provided the slope m is not zero. If a line is vertical, x = c, it intersects the x-axis at (c, 0) but has no y-intercept unless c = 0, in which case it passes through the origin.

Intercepts can also be described in intercept form for lines: x/a + y/b = 1, where a and b are the x- and y-intercepts, respectively. This form is useful for quickly visualizing where a line crosses the axes.

In higher dimensions, interceptos extend to intersections with coordinate planes. For a curve or surface, the interceptos with the axes help characterize its position and orientation relative to the coordinate system. The concept is widely used in graphing, analytic geometry, and related fields, and is connected to geometric relations such as the intercept theorem, which relates ratios of segments cut by parallels.