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Precalculus: Cartesian Coordinate System and Graphing

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Terms in this set (20)

  • What is the Cartesian Coordinate System?
    A rectangular coordinate system developed by Rene Descartes that visualizes numbers as points on a graph and equations as geometric figures.
  • How is a point represented in the Cartesian Coordinate System?
    Each point is represented by an ordered pair (x, y), where x is the distance from the origin along the x-axis and y is the distance along the y-axis.
  • Why is the pair (x, y) called an ordered pair?
    Because the order matters: the first number is the x-coordinate and the second is the y-coordinate.
  • What are the names of the horizontal and vertical axes in the Cartesian plane?
    The horizontal axis is called the x-axis and the vertical axis is called the y-axis.
  • What is the origin in the Cartesian Coordinate System?
    The point of intersection of the x-axis and y-axis, represented as (0, 0).
  • How many quadrants does the Cartesian plane have and what divides them?
    The plane is divided into 4 quadrants by the x-axis and y-axis.
  • What is the point-plotting method for graphing an equation?
    Plug each value of x into the equation to find y, then plot each ordered pair (x, y) and connect the points.
  • What is an x-intercept of a graph?
    The x-coordinate of a point where the graph crosses the x-axis; the y-coordinate at this point is always 0.
  • What is a y-intercept of a graph?
    The y-coordinate of a point where the graph crosses the y-axis; the x-coordinate at this point is always 0.
  • How do you find the x- and y-intercepts from a graph?
    Identify points where the graph crosses the axes: x-intercepts have y=0, y-intercepts have x=0.
  • What is the x-coordinate called in an ordered pair (x, y)?
    The x-coordinate.
  • What is the y-coordinate called in an ordered pair (x, y)?
    The y-coordinate.
  • What does it mean for an ordered pair to be a solution of an equation?
    When substituted into the equation, it makes the equation true.
  • What is the significance of the x-intercept's y-coordinate?
    It is always 0 because the point lies on the x-axis.
  • What is the significance of the y-intercept's x-coordinate?
    It is always 0 because the point lies on the y-axis.
  • How can graphs be used to determine intercepts?
    By locating where the graph crosses the x-axis and y-axis.
  • What does the graph of elevation vs. time illustrate in a story problem?
    It shows changes in elevation over time, such as walking uphill, downhill, or on level ground.
  • How do you interpret a graph showing temperature over time?
    By identifying times of highest and lowest temperatures and periods of increase or decrease.
  • What is the first step in graphing an equation using the point-plotting method?
    Choose values for x and calculate corresponding y values.
  • What is the role of the origin in plotting points?
    It serves as the reference point (0, 0) from which distances along axes are measured.