The y-axis is the vertical line on a two-dimensional or three-dimensional coordinate system, which helps to define the position of points in space. It plays a crucial role in representing the second variable in ordered pairs, while working in conjunction with the x-axis and z-axis to establish the framework for plotting and analyzing relationships among variables.
congrats on reading the definition of y-axis. now let's actually learn it.
The y-axis typically runs vertically and is used to measure the vertical distance from the origin in a coordinate system.
In a three-dimensional coordinate system, the y-axis is one of three axes, along with the x-axis and z-axis, which together define a point's location in space.
When graphing functions, the y-axis represents the output values or dependent variable, while the x-axis represents input values or independent variables.
Each point on the y-axis has coordinates of the form (0, y) when only considering two dimensions, indicating it lies directly above or below the origin.
In applications involving graphs and data visualization, the y-axis can represent various quantities like height, price, or time depending on the context of the problem.
Review Questions
How does the y-axis interact with other axes in a three-dimensional coordinate system?
In a three-dimensional coordinate system, the y-axis interacts with both the x-axis and z-axis to define a point's position in space. Each axis runs perpendicular to one another, allowing for a complete representation of any point using three coordinates: (x, y, z). The y-axis specifically represents vertical displacement and works alongside the x and z axes to facilitate spatial understanding and analysis.
Describe how you would determine a point's location using its coordinates involving the y-axis.
To determine a point's location using its coordinates involving the y-axis, you first identify its coordinates in the format (x, y) for two dimensions or (x, y, z) for three dimensions. The 'y' value indicates how far up or down from the origin (0, 0) on the vertical line of the y-axis that point lies. For three-dimensional points, you would also consider the 'z' value to ascertain depth relative to the x and y axes.
Evaluate how changes to values on the y-axis affect graphical representations of functions.
Changes to values on the y-axis significantly impact graphical representations of functions as they directly alter output values for given input values. If you increase or decrease these values while keeping x constant, you shift points up or down along the graph. This manipulation not only changes where a function intersects with horizontal lines but also affects critical features such as maxima and minima, ultimately altering interpretations of trends or behaviors of functions over specified intervals.
The axis in a three-dimensional coordinate system that runs perpendicular to both the x-axis and y-axis, representing the third variable.
coordinate plane: A two-dimensional surface formed by the intersection of the x-axis and y-axis, used for plotting points and visualizing mathematical relationships.