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The Rectangular Coordinate System quiz

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  • What is the rectangular coordinate system also called?
    It is also called the Cartesian plane.
  • How are points described in the rectangular coordinate system?
    Points are described as ordered pairs (x, y), where x is the horizontal coordinate and y is the vertical coordinate.
  • What is the origin in the rectangular coordinate system?
    The origin is the point (0, 0) where the x and y axes intersect.
  • What does a positive x and positive y value indicate about a point's location?
    It means the point is to the right and above the origin.
  • How do you plot the point (-3, 2) on the Cartesian plane?
    Move left 3 units on the x-axis, then up 2 units on the y-axis.
  • What are the four regions created by the x and y axes called?
    They are called quadrants.
  • Which quadrant is located in the top right corner of the Cartesian plane?
    Quadrant 1 is in the top right corner.
  • How do you verify if an ordered pair is a solution to a two-variable equation?
    Plug the x and y values into the equation and check if the resulting statement is true.
  • Is the ordered pair (5, 0) a solution to the equation x + 2y = 5?
    Yes, because 5 + 2*0 = 5, which is true.
  • Is the ordered pair (8, 2) a solution to the equation x + 2y = 5?
    No, because 8 + 2*2 = 12, which does not equal 5.
  • What is the process for completing an ordered pair when one value is missing?
    Plug the given value into the equation and solve for the missing variable.
  • If x = 1 in the equation y = 2x + 3, what is the corresponding y value?
    y = 2*1 + 3 = 5, so the ordered pair is (1, 5).
  • If y = -7 in the equation y = 2x + 3, what is the corresponding x value?
    x = (y - 3)/2 = (-7 - 3)/2 = -5, so the ordered pair is (-5, -7).
  • In the equation x = 3y - 2, if x = 2, what is the value of y?
    y = (x + 2)/3 = (2 + 2)/3 = 4/3.
  • In the equation x = 3y - 2, if y = 5, what is the value of x?
    x = 3*5 - 2 = 15 - 2 = 13.