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X-coordinate

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Intermediate Algebra

Definition

The x-coordinate is the horizontal position of a point on a coordinate plane. It represents the distance of a point from the y-axis and is the first value in an ordered pair that describes the location of a point.

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5 Must Know Facts For Your Next Test

  1. The x-coordinate is the first value in an ordered pair that describes the location of a point on a coordinate plane.
  2. The x-coordinate represents the horizontal position of a point and is the distance of the point from the y-axis.
  3. When graphing a linear equation, the x-coordinate of a point on the line corresponds to the input value for the independent variable.
  4. The x-coordinate is used to determine the domain of a function, which is the set of all possible input values.
  5. The x-coordinate is an essential component in the equation of a line, as it is used to calculate the y-coordinate through the slope-intercept form.

Review Questions

  • Explain how the x-coordinate is used to graph a linear equation in two variables.
    • When graphing a linear equation in two variables, the x-coordinate represents the independent variable. By substituting different x-values into the equation, you can calculate the corresponding y-values to plot points on the coordinate plane. The x-coordinates of these points determine the horizontal position of the line, while the y-coordinates determine the vertical position. The collection of these points forms the graph of the linear equation.
  • Describe the relationship between the x-coordinate and the domain of a function.
    • The x-coordinate is closely tied to the domain of a function, which is the set of all possible input values. The domain of a function is determined by the range of x-coordinates that can be used in the function's equation. For example, if a function is defined for all real numbers, its domain would include all possible x-coordinates. Conversely, if a function is defined only for positive integers, its domain would be limited to the set of positive integer x-coordinates.
  • Analyze how the x-coordinate is used to determine the equation of a line in slope-intercept form.
    • The slope-intercept form of a linear equation, $y = mx + b$, utilizes the x-coordinate to calculate the y-coordinate of a point on the line. The x-coordinate represents the independent variable, and by substituting different x-values into the equation, you can solve for the corresponding y-values. The slope, $m$, determines how the y-coordinate changes in relation to the x-coordinate, while the y-intercept, $b$, represents the point where the line crosses the y-axis. Together, the x-coordinate and the slope-intercept form provide a complete description of the line's equation and graph.
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