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# X and Y Coordinates – Definition, Examples

## What are x and y Coordinates?

In calculus, x and y coordinates represent the independent and dependent variables, respectively, in a function. The x coordinate is the input value, also known as the independent variable, and the y coordinate is the output value, also known as the dependent variable. The x coordinate represents the horizontal position on a graph, while the y coordinate represents the vertical position.

## X and Y Coordinates In Four Quadrants

In the context of a coordinate system, “X” and “Y” refer to two perpendicular lines, called axes, that intersect at a point called the origin. The “X” axis runs horizontally from left to right, while the “Y” axis runs vertically from bottom to top. The coordinate system is divided into four quadrants, which are labeled using Roman numerals (I, II, III, IV). Quadrant I is located in the upper right-hand corner, Quadrant II is in the upper left-hand corner, Quadrant III is in the lower left-hand corner, and Quadrant IV is in the lower right-hand corner.

## Plotting Points

To plot a point on a graph, we use the x and y coordinates to locate the point’s position. The x coordinate tells us the horizontal position, and the y coordinate tells us the vertical position. We plot the point by moving horizontally along the x-axis to the x coordinate and then vertically along the y-axis to the y coordinate.

### Functions

A function is a mathematical relationship between two variables, x and y. The value of y depends on the value of x. A function can be represented graphically by plotting points on a graph. Each point on the graph represents a pair of x and y coordinates that satisfy the equation of the function.

## Equations of Lines

The equation of a line in the Cartesian coordinate system can be represented as y = mx + b, where m is the slope of the line, and b is the y-intercept. The slope of a line is the change in y divided by the change in x, represented as (y2 – y1)/(x2 – x1). The y-intercept is the point where the line crosses the y-axis, and its value is represented by b.

## How to Find X and Y Coordinates?

To find the “X” and “Y” coordinates of a point on a coordinate system, you need to follow these steps:

1. Locate the point on the coordinate system.
2. Draw a straight line from the point to the “X” axis.
3. Draw a straight line from the point to the “Y” axis.
4. Measure the distance between the point and the origin along the “X” axis. This distance is the “X” coordinate.
5. Measure the distance between the point and the origin along the “Y” axis. This distance is the “Y” coordinate.

Note that the “X” coordinate is always written first, followed by the “Y” coordinate, and is usually written in parentheses. For example, the point (3, 4) has an “X” coordinate of 3 and a “Y” coordinate of 4.

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