Coordinate Plane

Definition

A coordinate plane is a two-dimensional surface defined by a horizontal axis (x-axis) and a vertical axis (y-axis) that intersect at a point called the origin. This structure allows for the representation of points, lines, and shapes in a numerical format, facilitating the analysis of linear equations and their graphical interpretations.

5 Must Know Facts For Your Next Test

1. The coordinate plane divides into four quadrants, numbered counterclockwise starting from the upper right quadrant.
2. Each point on the coordinate plane corresponds to an ordered pair, allowing for precise identification of its location based on its x and y values.
3. Linear equations can be graphically represented as straight lines on the coordinate plane, where the slope indicates the angle of the line.
4. Understanding how to plot points on the coordinate plane is crucial for solving and graphing linear equations effectively.
5. The distance between any two points on the coordinate plane can be calculated using the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$.

Review Questions

• How do you identify the location of a point on a coordinate plane?
  • To identify the location of a point on a coordinate plane, you use an ordered pair (x, y). The first number, 'x', indicates how far to move left or right from the origin along the x-axis, while the second number, 'y', shows how far to move up or down from that position along the y-axis. By following these directions, you can accurately pinpoint the location of any given point.
• What role does the slope play when graphing a linear equation on the coordinate plane?
  • The slope of a linear equation indicates how steeply a line rises or falls as it moves from left to right across the coordinate plane. It is calculated as 'rise over run', meaning it shows how much y changes for a given change in x. When graphing, this information helps determine the angle of the line and how it will intersect with both axes, thus shaping the overall visual representation of the equation.
• Evaluate how changes in a linear equation's coefficients affect its graph on the coordinate plane.
  • Changing the coefficients in a linear equation affects both its slope and y-intercept, which in turn alters its graph on the coordinate plane. For example, increasing the slope coefficient makes the line steeper, while changing the constant term shifts the line vertically. By analyzing these changes, one can better understand relationships between variables and predict how different scenarios will appear graphically.

Related terms

Origin: The point on the coordinate plane where the x-axis and y-axis intersect, represented as (0, 0).

Ordered Pair: A pair of numbers (x, y) used to locate a point on the coordinate plane, where 'x' represents the horizontal position and 'y' represents the vertical position.

Linear Equation:

An equation that models a straight line on the coordinate plane, typically expressed in the form y = mx + b, where m is the slope and b is the y-intercept.