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Study Guides > ALGEBRA / TRIG I

Summary: The Coordinate Plane

Key Concepts

  • Ordered Pair  An ordered pair, (x,y)\left(x,y\right) gives the coordinates of a point in a rectangular coordinate system.The first number is the x-coordinate.The second number is the y-coordinate.\begin{array}{c}\text{The first number is the }x\text{-coordinate}.\hfill \\ \text{The second number is the }y\text{-coordinate}.\hfill \end{array}
  • Steps for Plotting an Ordered Pair (x, y) in the Coordinate Plane
    • Determine the x-coordinate. Beginning at the origin, move horizontally, the direction of the x-axis, the distance given by the x-coordinate. If the x-coordinate is positive, move to the right; if the x-coordinate is negative, move to the left.
    • Determine the y-coordinate. Beginning at the x-coordinate, move vertically, the direction of the y-axis, the distance given by the y-coordinate. If the y-coordinate is positive, move up; if the y-coordinate is negative, move down.
    • Draw a point at the ending location. Label the point with the ordered pair.
    • An ordered pair is represented by a single point on the graph.
  • Sign Patterns of the Quadrants
    Quadrant I Quadrant II Quadrant III Quadrant IV
    (x,y)(x,y) (x,y)(x,y) (x,y)(x,y) (x,y)(x,y)
    (+,+)(+,+) (,+)(−,+) (,)(−,−) (+,)(+,−)
  • Coordinates of Zero
    • Points with a yy-coordinate equal to 00 are on the x-axis, and have coordinates (a,0) (a, 0).
    • Points with a xx-coordinate equal to 00 are on the y-axis, and have coordinates (0,b)(0, b).
    • The point (0,0)(0, 0) is called the origin. It is the point where the x-axis and y-axis intersect.
  • Identifying Solutions  To find out whether an ordered pair is a solution of a linear equation, you can do the following:

    • Graph the linear equation, and graph the ordered pair. If the ordered pair appears to be on the graph of a line, then it is a possible solution of the linear equation. If the ordered pair does not lie on the graph of a line, then it is not a solution.
    • Substitute the (x, y) values into the equation. If the equation yields a true statement, then the ordered pair is a solution of the linear equation. If the ordered pair does not yield a true statement then it is not a solution.

Glossary

linear equation
An equation of the form Ax+By=CAx+By=C, where AA and BB are not both zero, is called a linear equation in two variables.
ordered pair
An ordered pair (x,y)\left(x,y\right) gives the coordinates of a point in a rectangular coordinate system. The first number is the xx -coordinate. The second number is the yy -coordinate. (x,y)x-coordinate,y-coordinate\underset{x\text{-coordinate},y\text{-coordinate}}{\left(x,y\right)}
origin
The point (0,0)\left(0,0\right) is called the origin. It is the point where the the point where the xx -axis and yy -axis intersect.
quadrants
The xx -axis and yy -axis divide a rectangular coordinate system into four areas, called quadrants.  The quadrants are labeled with the Roman Numerals I, II, III, IV going around the coordinate system in a counter-clockwise direction.
solution to a linear equation in two variables
An ordered pair (x,y)\left(x,y\right) is a solution to the linear equation Ax+By=CAx+By=C, if the equation is a true statement when the x- and y-values of the ordered pair are substituted into the equation.
x-axis
The x-axis is the horizontal axis in a rectangular coordinate system.
y-axis
The y-axis is the vertical axis on a rectangular coordinate system.

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